Riemannian invariants for warped product submanifolds in Q ε m × R {{\mathbb{Q}}}_{\varepsilon }^{m}\times {\mathbb{R}} and their applications

Open Mathematics, Journal Year: 2024, Volume and Issue: 22(1)

Published: Jan. 1, 2024

Abstract This article investigates the geometric and topologic of warped product submanifolds in Riemannian Q ε m × mathvariant="double-struck">R {{\mathbb{Q}}}_{\varepsilon }^{m}\times {\mathbb{R}} . In this respect, we obtain first Chen inequality that involves extrinsic invariants like length warping functions mean curvature. two intrinsic (sectional curvature δ \delta -invariant). addition, an integral bound is provided for Bochner operator formula compact terms Ricci gradient. We aim to apply theory many structures Dirichlet eigenvalues problem applications. Some new results regarding vanishing are presented as a partial solution, can be considered well-known given by Chern.

Language: Английский

Ricci flow of Kaehlerian slant submanifolds in complex space forms and its applications

Arabian Journal of Mathematics, Journal Year: 2024, Volume and Issue: unknown

Published: Oct. 12, 2024

Abstract The normalized Ricci flow converges to a constant curvature metric for connected Kaehlerian slant submanifold in complex space form if the squared norm of second fundamental satisfies certain upper bounds. These bounds include sectional curvature, angle, and mean vector. Additionally, we demonstrate that is diffeomorphic sphere $$\mathbb {S}^{n_1}$$ S n 1 under some restriction on curvature. We claim our previous results are rare cases.

Language: Английский