An Invariant of Riemannian Type for Legendrian Warped Product Submanifolds of Sasakian Space Forms

Fatemah Abdullah Alghamdi, Lamia Saeed Alqahtani, Ali H. Alkhaldi and Akram Ali ()
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Fatemah Abdullah Alghamdi: Financial Sciences Department, Applied College, Imam Abdulrahman Bin Faisal University, Dammam 31441, Saudi Arabia
Lamia Saeed Alqahtani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ali H. Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia

Mathematics, 2023, vol. 11, issue 23, 1-20

Abstract: In the present paper, we investigate the geometry and topology of warped product Legendrian submanifolds in Sasakian space forms D 2 n + 1 ( ? ) and obtain the first Chen inequality that involves extrinsic invariants like the mean curvature and the length of the warping functions. This inequality also involves intrinsic invariants ( ? -invariant and sectional curvature). In addition, an integral bound is provided for the Bochner operator formula of compact warped product submanifolds in terms of the gradient Ricci curvature. Some new results on mean curvature vanishing are presented as a partial solution to the well-known problem given by S.S. Chern.

Keywords: warped products; Legendrian; Sasakian space form; Ricci curvature; ordinary differential equations; Riemannian invariants; Bochner operator formula; eigenvalues (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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