preprints.org > computer science and mathematics > geometry and topology > doi: 10.20944/preprints202304.1148.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 28 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (08:40:49 CEST)

A class of nearly Sasakian manifolds is considered. We discussion geometric effects of some symmetries on such manifolds, and show, under a certain condition, that the class of Ricci-symmetric nearly Sasakian manifolds is a subclass of Einstein manifolds. We prove that a nearly Sasakian space form with Ricci tensor satisfying the Codazzi equation is either a Sasakian manifold with a constant $\phi$-holomorphic sectional curvature $\mathcal{H}=1$ or a $5$-dimensional proper nearly Sasakian manifold with a constant $\phi$-holomorphic sectional curvature $\mathcal{H}>1$. We also prove that the spectrum of the operator $H^{2}$ generated by the nearly Sasakian manifold is a set of simple eigenvalue $0$ and an eigenvalue of multiplicity $4$. We show that there exist integrable distributions on the same manifolds with totally geodesic leaves, and prove that there are no proper nearly Sasakian space forms with constant sectional curvature.

Nearly Sasakian space forms; k-nullity distribution; locally symmetric manifold; semi-symmetric manifold; Ricci-symmetric manifold

Computer Science and Mathematics, Geometry and Topology

* All users must log in before leaving a comment