On a Sequence of Slant Submanifolds in Almost Product Riemannian Setting

Year 2023, Volume: 16 Issue: 2, 594 - 597, 29.10.2023

Adara M. Blaga

https://doi.org/10.36890/iejg.1321401

Abstract

We prove that the property of being pointwise slant is transitive on a class of proper pointwise slant submanifolds of almost product Riemannian manifolds, and illustrate this fact with an example. For a given almost product Riemannian manifold $(M_1,g,\varphi_1)$, we consider a sequence of pointwise slant submanifolds $(M_{i+1}\hookrightarrow M_i)_{i\in \mathbb{N}^*}$, and we explicitly determine the relation between the slant functions. Moreover, we state this result in a more general case.

Keywords

Pointwise slant submanifold, almost product Riemannian manifold, anti-invariant submanifold

References

• [1] Blaga, A.M.: New insights on slant submanifolds in almost Hermitian geometry. (2023). https://doi.org/10.48550/arXiv.2306.04982
• [2] Chen, B.-Y., Garay, O.J.: Pointwise slant submanifolds in almost Hermitian manifolds. Turkish J. Math. 36, 630–640 (2012). https://doi.org/10.3906/mat-1101-34
• [3] Etayo, F.: On quasi-slant submanifolds of an almost Hermitian manifold. Publ. Math. Debrecen. 53(1-2), 217–223 (1998).