A note on quasi-bi-slant submanifolds of Sasakian manifolds

Abstract

The object of the present paper is to study the notion of quasi-bi-slant submanifolds of almost contact metric manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant, and quasi-hemi-slant submanifolds. We study and characterize quasi-bi-slant submanifolds of Sasakian manifolds and provide non-trivial examples to signify that the structure presented in this paper is valid. Furthermore, the integrability of distributions and geometry of foliations are researched. Moreover, we characterize quasi-bi-slant submanifolds with parallel canonical structures.

Aspects of Submanifolds on (α, β)-Type Almost Contact Manifolds with Quasi-Hemi-Slant Factor

“…A (1, 0) type of trans-Sasakian manifold is clearly a Sasakian manifold [30], whereas a (0, 1) type of trans-Sasakian manifold is obviously a Kenmotsu manifold [31]. A (0, 0) type of trans-Sasakian manifold is a cosymplectic manifold [25].…”

“…On different types of differentiable manifolds, the slant submanifolds were further extended as pseudo-slant submanifolds, semi-slant submanifolds, bi-slant submanifolds, and quasi-slant submanifolds [19][20][21][22][23][24]. Prasad et al [25,26] recently researched the quasihemi-slant submanifolds of cosymplectic manifolds and Sasakian manifolds, as well as the features of integrability of distribution and completely geodesic manifolds.…”

Pointwise Quasi Hemi-Slant Submanifolds of Cosymplectic Manifolds

“…Then, the theory of submanifolds is investigated by many geometers like [6][7][8][9][10][11][12][13][14]. As a generalization of slant submanifolds; semi-slant submanifolds, hemi-slant submanifolds, bislant submanifolds, quasi bi-slant submanifolds, quasi hemi-slant submanifolds, pointwise quasi bi-slant submanifolds, PQHS submanifolds [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and many others. In 2013, B. Şahin defined the concept of pointwise semi-slant submanifolds [30].…”