Abstract
In this paper, we give an estimate of the first eigenvalue of the Laplace operator on minimally immersed Legendrian submanifold N n in Sasakian space forms N ˜ 2 n + 1 ( ϵ ) . We prove that a minimal Legendrian submanifolds in a Sasakian space form is isometric to a standard sphere S n if the Ricci curvature satisfies an extrinsic condition which includes a gradient of a function, the constant holomorphic sectional curvature of the ambient space and a dimension of N n . We also obtain a Simons-type inequality for the same ambient space forms N ˜ 2 n + 1 ( ϵ ) .
Funder
King Khalid University
Princess Nourah bint Abdulrahman University
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
14 articles.
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