id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-2204	Shadab Ahmad Khan	A New Type of (ϵ)- Lorentzian Para-Sasakian Manifolds	2024	13	.pdf	application/pdf	4491	246	72	[𝑔(𝑌, 𝑍)𝑔(𝑋,𝑊) − 𝑔(𝑋, 𝑍)𝑔(𝑌,𝑊)] 𝑔(𝑅(𝑋, 𝑌)𝑍,𝑊) = { 𝑟 − 2𝜖(𝑛 − 1)(𝛼2 + 𝛽2) (𝑛 − 1)(𝑛 − 2) } { 𝑔(𝑌, 𝑍)𝑔(𝑋,𝑊) − 𝑔(𝑋, 𝑍)𝑔(𝑌,𝑊) } + { 𝑟 − 𝜖𝑛(𝑛 − 1)(𝛼2 + 𝛽2) (𝑛 − 1)(𝑛 − 2) } { 𝜂(𝑌)𝜂(𝑍)𝑔(𝑋,𝑊) −𝜂(𝑋)𝜂(𝑍)𝑔(𝑌,𝑊) +𝜂(𝑋)𝜂(𝑊)𝑔(𝑌, 𝑍) −𝜂(𝑌)𝜂(𝑊)}𝑔(𝑋, 𝑍)} In view of definition (2.1) and above relation, we have the following. Let us suppose 𝐹(𝑋, 𝑌) = 𝑝𝑔(𝑋, 𝑌) + 𝑞 (𝑋)𝜂(𝑌) (4.6) where, 𝑝 = √{ 𝑟 − 2𝜖(𝑛 − 1)(𝛼2 + 𝛽2) (𝑛 − 1)(𝑛 − 2) } and 𝑞 = { 𝑟 − 𝜖𝑛(𝑛 − 1)(𝛼2 + 𝛽2) (𝑛 − 1)(𝑛 − 2) }√{ (𝑛 − 1)(𝑛 − 2) 𝑟 − 2𝜖(𝑛 − 1)(𝛼2 + 𝛽2) } Now, from the equation (2.13), we have �̃�(𝑋, 𝑌, 𝑍,𝑊) = 𝐹(𝑌, 𝑍)𝐹(𝑋,𝑊) − 𝐹(𝑋, 𝑍)𝐹(𝑌,𝑊)	cache/cana-2204.pdf	txt/cana-2204.txt