id	sid	eid	entity	type
ejpam-3177	1	1	european journal	ORG
ejpam-3177	2	1	11	CARDINAL
ejpam-3177	2	2	1, 2018	DATE
ejpam-3177	2	3	150	CARDINAL
ejpam-3177	2	4	1307-5543	CARDINAL
ejpam-3177	2	5	new york	GPE
ejpam-3177	2	6	global biharmonic maps	ORG
ejpam-3177	2	7	abdul rehman1,∗	PERSON
ejpam-3177	2	8	bari2 1	PRODUCT
ejpam-3177	2	9	sahiwal	GPE
ejpam-3177	2	10	pakistan 2	ORG
ejpam-3177	2	11	bahawalpur	PERSON
ejpam-3177	2	12	pakistan	GPE
ejpam-3177	3	1	second	ORDINAL
ejpam-3177	4	1	2010	DATE
ejpam-3177	4	2	53c55	CARDINAL
ejpam-3177	4	3	53c43	DATE
ejpam-3177	4	4	58e20	CARDINAL
ejpam-3177	4	5	s-manifolds	ORG
ejpam-3177	4	6	biharmonic maps 1	ORG
ejpam-3177	5	1	between riemannian manifolds	MONEY
ejpam-3177	5	2	last decades	DATE
ejpam-3177	5	3	j. eells	PERSON
ejpam-3177	5	4	j.h. sampson	PERSON
ejpam-3177	8	1	riemannian manifolds	ORG
ejpam-3177	8	2	13	CARDINAL
ejpam-3177	9	1	14	CARDINAL
ejpam-3177	10	1	6	CARDINAL
ejpam-3177	11	1	10	CARDINAL
ejpam-3177	11	2	11	CARDINAL
ejpam-3177	11	3	12	CARDINAL
ejpam-3177	12	1	15	CARDINAL
ejpam-3177	13	1	16	CARDINAL
ejpam-3177	14	1	biharmonic	NORP
ejpam-3177	15	1	1862	DATE
ejpam-3177	15	2	maxwell	ORG
ejpam-3177	16	1	euler	PERSON
ejpam-3177	16	2	first	ORDINAL
ejpam-3177	16	3	1986	DATE
ejpam-3177	16	4	8	CARDINAL
ejpam-3177	17	1	2	CARDINAL
ejpam-3177	17	2	3	CARDINAL
ejpam-3177	17	3	5	CARDINAL
ejpam-3177	18	1	5	CARDINAL
ejpam-3177	18	2	the biharmonic submanifolds	ORG
ejpam-3177	19	1	second	ORDINAL
ejpam-3177	20	1	biharmonic maps	ORG
ejpam-3177	20	2	s-manifolds	ORG
ejpam-3177	20	3	third	ORDINAL
ejpam-3177	22	1	n. a. rehman	PERSON
ejpam-3177	22	2	m. bari	PERSON
ejpam-3177	23	1	150	CARDINAL
ejpam-3177	23	2	2018	DATE
ejpam-3177	24	1	n. a. rehman	PERSON
ejpam-3177	24	2	m. bari	PERSON
ejpam-3177	25	1	j. pure	PERSON
ejpam-3177	25	2	11	CARDINAL
ejpam-3177	25	3	1	CARDINAL
ejpam-3177	25	4	2018	DATE
ejpam-3177	25	5	150	CARDINAL
ejpam-3177	25	6	biharmonic maps	ORG
ejpam-3177	25	7	s-manifolds	ORG
ejpam-3177	26	1	between two riemannian manifolds	MONEY
ejpam-3177	28	1	7	CARDINAL
ejpam-3177	28	2	1 2	CARDINAL
ejpam-3177	28	3	1 2 m∑	QUANTITY
ejpam-3177	32	1	e(f	PERSON
ejpam-3177	32	2	∈	ORG
ejpam-3177	34	1	euler	PERSON
ejpam-3177	34	2	τ(f	ORG
ejpam-3177	34	3	τ(f	ORG
ejpam-3177	34	4	τ(f	ORG
ejpam-3177	35	1	levi	PERSON
ejpam-3177	35	2	levi civita	PERSON
ejpam-3177	35	3	two	CARDINAL
ejpam-3177	36	1	w.	PERSON
ejpam-3177	36	2	second	ORDINAL
ejpam-3177	36	3	∂2	CARDINAL
ejpam-3177	39	1	jf	PERSON
ejpam-3177	39	2	second	ORDINAL
ejpam-3177	40	1	jf	PERSON
ejpam-3177	41	1	1	CARDINAL
ejpam-3177	43	1	9	CARDINAL
ejpam-3177	44	1	j. eells	PERSON
ejpam-3177	44	2	l. lemaire	PERSON
ejpam-3177	45	1	9	CARDINAL
ejpam-3177	45	2	jiang	PERSON
ejpam-3177	46	1	8	CARDINAL
ejpam-3177	46	2	n. a. rehman	PERSON
ejpam-3177	46	3	m. bari	PERSON
ejpam-3177	47	1	j. pure	PERSON
ejpam-3177	47	2	11	CARDINAL
ejpam-3177	47	3	1	CARDINAL
ejpam-3177	47	4	2018	DATE
ejpam-3177	47	5	150	CARDINAL
ejpam-3177	47	6	first	ORDINAL
ejpam-3177	47	7	second	ORDINAL
ejpam-3177	47	8	biharmonic maps	ORG
ejpam-3177	48	1	1 2	CARDINAL
ejpam-3177	49	1	2	CARDINAL
ejpam-3177	49	2	γ(f−1tn	ORG
ejpam-3177	50	1	first	ORDINAL
ejpam-3177	51	1	h(τ2(f	GPE
ejpam-3177	51	2	3	CARDINAL
ejpam-3177	51	3	j(τ(f	PERSON
ejpam-3177	52	1	4̄(τ(f	CARDINAL
ejpam-3177	52	2	−r(τ(f	PERSON
ejpam-3177	52	3	4	CARDINAL
ejpam-3177	52	4	j	PERSON
ejpam-3177	52	5	1	CARDINAL
ejpam-3177	53	1	biharmonic if τ2(f	ORG
ejpam-3177	54	1	0	CARDINAL
ejpam-3177	55	1	17	CARDINAL
ejpam-3177	55	2	2n + s	QUANTITY
ejpam-3177	55	3	1,1	CARDINAL
ejpam-3177	55	4	2n	CARDINAL
ejpam-3177	55	5	0	CARDINAL
ejpam-3177	57	1	2n +	DATE
ejpam-3177	57	2	2n	CARDINAL
ejpam-3177	61	1	0	CARDINAL
ejpam-3177	62	1	⊗ ηα	PERSON
ejpam-3177	62	2	5	CARDINAL
ejpam-3177	62	3	1	CARDINAL
ejpam-3177	66	1	1	CARDINAL
ejpam-3177	68	1	⊗ dηα	PERSON
ejpam-3177	69	1	2	CARDINAL
ejpam-3177	69	2	ω(x	DATE
ejpam-3177	71	1	ω	ORG
ejpam-3177	71	2	η1∧	PERSON
ejpam-3177	71	3	dη1 = ·	PERSON
ejpam-3177	72	1	dηs = ω	PERSON
ejpam-3177	74	1	manifolds	ORG
ejpam-3177	74	2	blair	PERSON
ejpam-3177	74	3	1	CARDINAL
ejpam-3177	75	1	n. a. rehman	PERSON
ejpam-3177	75	2	m. bari	PERSON
ejpam-3177	76	1	j. pure	PERSON
ejpam-3177	76	2	11	CARDINAL
ejpam-3177	76	3	1	CARDINAL
ejpam-3177	76	4	2018	DATE
ejpam-3177	76	5	150	CARDINAL
ejpam-3177	76	6	1	CARDINAL
ejpam-3177	76	7	s-manifolds	ORG
ejpam-3177	76	8	sasakian manifolds	ORG
ejpam-3177	77	1	2	CARDINAL
ejpam-3177	77	2	1	CARDINAL
ejpam-3177	78	1	1	CARDINAL
ejpam-3177	78	2	∈	ORG
ejpam-3177	78	3	1	CARDINAL
ejpam-3177	80	1	6	CARDINAL
ejpam-3177	80	2	g(fx	PRODUCT
ejpam-3177	81	1	7	CARDINAL
ejpam-3177	82	1	ξ1	NORP
ejpam-3177	85	1	0	CARDINAL
ejpam-3177	88	1	g(fs	ORG
ejpam-3177	89	1	− g(fs	PERSON
ejpam-3177	91	1	− g(fs	PERSON
ejpam-3177	92	1	− ω(s	PERSON
ejpam-3177	92	2	w	GPE
ejpam-3177	92	3	8)	CARDINAL
ejpam-3177	92	4	w ∈	ORG
ejpam-3177	93	1	2	CARDINAL
ejpam-3177	94	1	n(k	PERSON
ejpam-3177	95	1	e2n+s	PRODUCT
ejpam-3177	96	1	∈	ORG
ejpam-3177	96	2	∈	ORG
ejpam-3177	97	1	∈	ORG
ejpam-3177	98	1	tx + nx	ORG
ejpam-3177	98	2	tx	ORG
ejpam-3177	98	3	4	CARDINAL
ejpam-3177	102	1	two	CARDINAL
ejpam-3177	105	1	•	CARDINAL
ejpam-3177	105	2	⊆	CARDINAL
ejpam-3177	108	1	4	CARDINAL
ejpam-3177	109	1	n. a. rehman	PERSON
ejpam-3177	109	2	m. bari	PERSON
ejpam-3177	110	1	j. pure	PERSON
ejpam-3177	110	2	11	CARDINAL
ejpam-3177	110	3	1	CARDINAL
ejpam-3177	110	4	2018	DATE
ejpam-3177	110	5	150	CARDINAL
ejpam-3177	110	6	biharmonic maps	ORG
ejpam-3177	110	7	jiang	PERSON
ejpam-3177	110	8	1	CARDINAL
ejpam-3177	111	1	8	CARDINAL
ejpam-3177	111	2	mm	PERSON
ejpam-3177	111	3	1 mτ(f	CARDINAL
ejpam-3177	111	4	f.	PERSON
ejpam-3177	111	5	4τ(f	GPE
ejpam-3177	113	1	df(ej))(∇̃eidf)(ej	ORG
ejpam-3177	114	1	2	CARDINAL
ejpam-3177	115	1	8	CARDINAL
ejpam-3177	115	2	mm	PERSON
ejpam-3177	115	3	1 mτ(f	CARDINAL
ejpam-3177	115	4	f.	PERSON
ejpam-3177	115	5	4τ(f	GPE
ejpam-3177	116	1	k=1 h(τ(f	PERSON
ejpam-3177	116	2	df(ek))df(ej)df(ek)− − m∑	PERSON
ejpam-3177	118	1	3	CARDINAL
ejpam-3177	119	1	8	CARDINAL
ejpam-3177	119	2	mm	PERSON
ejpam-3177	119	3	nm+1	GPE
ejpam-3177	120	1	∇xτ(f	ORG
ejpam-3177	120	2	5	CARDINAL
ejpam-3177	120	3	8	CARDINAL
ejpam-3177	121	1	3.1	CARDINAL
ejpam-3177	121	2	1	CARDINAL
ejpam-3177	122	1	2m+s	CARDINAL
ejpam-3177	122	2	2n+s	CARDINAL
ejpam-3177	122	3	φ	ORG
ejpam-3177	122	4	zero	CARDINAL
ejpam-3177	122	5	φ	ORG
ejpam-3177	122	6	• ‖ b(φ	WORK_OF_ART
ejpam-3177	123	1	4	DATE
ejpam-3177	123	2	2m=2n-1 •	CARDINAL
ejpam-3177	124	1	n n. a. rehman	PERSON
ejpam-3177	124	2	m. bari	PERSON
ejpam-3177	125	1	j. pure	PERSON
ejpam-3177	125	2	11	CARDINAL
ejpam-3177	125	3	1	CARDINAL
ejpam-3177	125	4	2018	DATE
ejpam-3177	125	5	150	CARDINAL
ejpam-3177	128	1	−f2dφ(vj)ηα(dφvk)ηβ(dφvk)− h(fdφvj	GPE
ejpam-3177	134	1	+ h(fdφvj	GPE
ejpam-3177	134	2	fdφvk)f 2dφ(vk	PERSON
ejpam-3177	135	1	+ 2fdφ(vk)h(dφvj	DATE
ejpam-3177	135	2	1 4	DATE
ejpam-3177	139	1	k=1 h(τ(φ	PERSON
ejpam-3177	139	2	1 4	DATE
ejpam-3177	141	1	9	CARDINAL
ejpam-3177	141	2	τ(φ	ORG
ejpam-3177	141	3	τ(φ	ORG
ejpam-3177	143	1	s-manifolds	ORG
ejpam-3177	144	1	τ(φ	ORG
ejpam-3177	146	1	2	CARDINAL
ejpam-3177	146	2	2n	CARDINAL
ejpam-3177	146	3	1	CARDINAL
ejpam-3177	148	1	2n−1+s∑	CARDINAL
ejpam-3177	149	1	lemma 2,	ORG
ejpam-3177	150	1	2n−1+s∑	CARDINAL
ejpam-3177	150	2	τ(f	ORG
ejpam-3177	150	3	∇̃vidφ)(vj	ORG
ejpam-3177	151	1	n. a. rehman	PERSON
ejpam-3177	151	2	m. bari	PERSON
ejpam-3177	152	1	j. pure	PERSON
ejpam-3177	152	2	11	CARDINAL
ejpam-3177	152	3	1	CARDINAL
ejpam-3177	152	4	2018	DATE
ejpam-3177	152	5	150	CARDINAL
ejpam-3177	152	6	r(τ(φ	GPE
ejpam-3177	154	1	2n−1+s∑ k=1 rn	QUANTITY
ejpam-3177	154	2	τ(φ	ORG
ejpam-3177	154	3	= k	PERSON
ejpam-3177	155	1	+ 3s 4	PERCENT
ejpam-3177	155	2	1 +	CARDINAL
ejpam-3177	155	3	τ(φ	ORG
ejpam-3177	156	1	10	CARDINAL
ejpam-3177	158	1	0	CARDINAL
ejpam-3177	158	2	11	CARDINAL
ejpam-3177	158	3	2n−1+s∑	CARDINAL
ejpam-3177	159	1	τ(f	ORG
ejpam-3177	159	2	+ 3s 4	PERCENT
ejpam-3177	159	3	1 +	CARDINAL
ejpam-3177	159	4	τ(φ	ORG
ejpam-3177	160	1	0(12	CARDINAL
ejpam-3177	162	1	dφ(vk))v = hjku	ORG
ejpam-3177	163	1	τ(f	ORG
ejpam-3177	163	2	2n−1+s∑	CARDINAL
ejpam-3177	163	3	2n−1+s∑	CARDINAL
ejpam-3177	164	1	15	CARDINAL
ejpam-3177	164	2	2n−1+s∑	CARDINAL
ejpam-3177	165	1	1 +	CARDINAL
ejpam-3177	165	2	τ(φ	ORG
ejpam-3177	165	3	0	CARDINAL
ejpam-3177	165	4	k=1 hjkhjku	PERSON
ejpam-3177	166	1	4	CARDINAL
ejpam-3177	166	2	τ(φ	ORG
ejpam-3177	167	1	4	CARDINAL
ejpam-3177	167	2	0	CARDINAL
ejpam-3177	167	3	τ(φ	ORG
ejpam-3177	170	1	0	CARDINAL
ejpam-3177	172	1	4	CARDINAL
ejpam-3177	173	1	13	CARDINAL
ejpam-3177	173	2	n. a. rehman	PERSON
ejpam-3177	173	3	m. bari	PERSON
ejpam-3177	174	1	j. pure	PERSON
ejpam-3177	174	2	11	CARDINAL
ejpam-3177	174	3	1	CARDINAL
ejpam-3177	174	4	2018	DATE
ejpam-3177	174	5	150	CARDINAL
ejpam-3177	174	6	τ(φ	ORG
ejpam-3177	174	7	γtm⊥.	ORG
ejpam-3177	175	1	0	CARDINAL
ejpam-3177	177	1	2n−1+s∑ k=1 rn	QUANTITY
ejpam-3177	177	2	τ(φ	ORG
ejpam-3177	177	3	= k	PERSON
ejpam-3177	178	1	+ 3s 4	PERCENT
ejpam-3177	179	1	14	CARDINAL
ejpam-3177	179	2	11	CARDINAL
ejpam-3177	179	3	2m+s∑	CARDINAL
ejpam-3177	179	4	τ(f	ORG
ejpam-3177	180	1	+ 3s 4	PERCENT
ejpam-3177	180	2	0	CARDINAL
ejpam-3177	180	3	15	CARDINAL
ejpam-3177	180	4	τ(φ	ORG
ejpam-3177	182	1	0	CARDINAL
ejpam-3177	185	1	1	CARDINAL
ejpam-3177	186	1	2n−1	CARDINAL
ejpam-3177	186	2	2n	CARDINAL
ejpam-3177	186	3	φ	ORG
ejpam-3177	186	4	zero	CARDINAL
ejpam-3177	186	5	φ	ORG
ejpam-3177	187	1	1	CARDINAL
ejpam-3177	188	1	13	CARDINAL
ejpam-3177	189	1	2	CARDINAL
ejpam-3177	190	1	2n	CARDINAL
ejpam-3177	190	2	1	CARDINAL
ejpam-3177	190	3	2n+1	PRODUCT
ejpam-3177	190	4	φ	ORG
ejpam-3177	190	5	zero	CARDINAL
ejpam-3177	190	6	φ	ORG
ejpam-3177	192	1	13	CARDINAL
ejpam-3177	193	1	first	ORDINAL
ejpam-3177	193	2	pakistan	GPE
ejpam-3177	194	1	158	CARDINAL
ejpam-3177	194	2	1	CARDINAL
ejpam-3177	194	3	d.e. blair	ORG
ejpam-3177	194	4	manifolds	ORG
ejpam-3177	194	5	j. differential geom	PERSON
ejpam-3177	195	1	4 (1970	DATE
ejpam-3177	196	1	155	CARDINAL
ejpam-3177	197	1	2	CARDINAL
ejpam-3177	197	2	a. balmus	PERSON
ejpam-3177	197	3	biharmonic properties	ORG
ejpam-3177	198	1	univ.	ORG
ejpam-3177	201	1	n.s.	GPE
ejpam-3177	202	1	50	CARDINAL
ejpam-3177	202	2	2004	DATE
ejpam-3177	202	3	361372	DATE
ejpam-3177	203	1	3	CARDINAL
ejpam-3177	203	2	a. balmus	PERSON
ejpam-3177	203	3	the biharmonic submanifolds of s3	ORG
ejpam-3177	204	1	univ.	ORG
ejpam-3177	207	1	51	DATE
ejpam-3177	207	2	171190	DATE
ejpam-3177	208	1	4	CARDINAL
ejpam-3177	208	2	jose l. cabrerizo	PERSON
ejpam-3177	208	3	luis m. fernandez	PERSON
ejpam-3177	208	4	manuel fernandez	PERSON
ejpam-3177	208	5	s-manifolds	ORG
ejpam-3177	208	6	colloquim mathematicum	PERSON
ejpam-3177	208	7	lxiv	ORG
ejpam-3177	208	8	1993	DATE
ejpam-3177	208	9	2.	CARDINAL
ejpam-3177	209	1	5	CARDINAL
ejpam-3177	209	2	toshiyuki ichiyama	PERSON
ejpam-3177	209	3	jun-ichi inoguchi	ORG
ejpam-3177	209	4	di matematica	PERSON
ejpam-3177	210	1	1	CARDINAL
ejpam-3177	210	2	233-275	CARDINAL
ejpam-3177	211	1	6	CARDINAL
ejpam-3177	211	2	j. davidov	PERSON
ejpam-3177	211	3	a. g. sergeev	PERSON
ejpam-3177	211	4	1993	DATE
ejpam-3177	211	5	48	CARDINAL
ejpam-3177	211	6	3(291	CARDINAL
ejpam-3177	211	7	396	CARDINAL
ejpam-3177	212	1	7	CARDINAL
ejpam-3177	212	2	j. eells	PERSON
ejpam-3177	212	3	j. h. sampson	PERSON
ejpam-3177	212	4	amer	PERSON
ejpam-3177	212	5	j. math	PERSON
ejpam-3177	213	1	86 (1964	DATE
ejpam-3177	213	2	109-160	CARDINAL
ejpam-3177	213	3	8	CARDINAL
ejpam-3177	213	4	g. y. jiang	PERSON
ejpam-3177	214	1	2	CARDINAL
ejpam-3177	214	2	first	ORDINAL
ejpam-3177	214	3	second	ORDINAL
ejpam-3177	214	4	chinese	NORP
ejpam-3177	215	1	1986	DATE
ejpam-3177	215	2	389	CARDINAL
ejpam-3177	216	1	9	CARDINAL
ejpam-3177	216	2	j. eells	PERSON
ejpam-3177	216	3	l. lemaire	PERSON
ejpam-3177	216	4	bull	ORG
ejpam-3177	216	5	london	GPE
ejpam-3177	218	1	20 (1988	DATE
ejpam-3177	218	2	385	CARDINAL
ejpam-3177	219	1	10	CARDINAL
ejpam-3177	219	2	cosymplectic manifolds	ORG
ejpam-3177	219	3	40	DATE
ejpam-3177	219	4	247	CARDINAL
ejpam-3177	220	1	11	CARDINAL
ejpam-3177	220	2	c. gherghe	PERSON
ejpam-3177	220	3	s. ianus	PERSON
ejpam-3177	220	4	a. m. pastore	PERSON
ejpam-3177	221	1	42	CARDINAL
ejpam-3177	222	1	12	CARDINAL
ejpam-3177	222	2	c-manifolds	ORG
ejpam-3177	223	1	geom	PERSON
ejpam-3177	225	1	55-63	CARDINAL
ejpam-3177	226	1	13	CARDINAL
ejpam-3177	226	2	a. lichnerowicz	PERSON
ejpam-3177	228	1	3	CARDINAL
ejpam-3177	228	2	341402	DATE
ejpam-3177	229	1	14	CARDINAL
ejpam-3177	229	2	j. rawnsley	PERSON
ejpam-3177	229	3	1164	DATE
ejpam-3177	229	4	1984	DATE
ejpam-3177	229	5	85159	DATE
ejpam-3177	230	1	15	CARDINAL
ejpam-3177	230	2	n.a. rehman	ORG
ejpam-3177	230	3	s-manifolds	ORG
ejpam-3177	230	4	st.	GPE
ejpam-3177	230	5	univ	NORP
ejpam-3177	231	1	ovidius constanta	PERSON
ejpam-3177	231	2	2013	DATE
ejpam-3177	231	3	197	CARDINAL
ejpam-3177	232	1	16	CARDINAL
ejpam-3177	232	2	biharmonic maps	ORG
ejpam-3177	232	3	2015	DATE
ejpam-3177	232	4	7	CARDINAL
ejpam-3177	232	5	651	CARDINAL
ejpam-3177	233	1	159	CARDINAL
ejpam-3177	233	2	17	CARDINAL
ejpam-3177	233	3	k. yano	PERSON
ejpam-3177	233	4	m. kon	PERSON
ejpam-3177	233	5	manifolds	ORG
ejpam-3177	233	6	3	CARDINAL
ejpam-3177	233	7	singapore	GPE
ejpam-3177	233	8	1984	DATE