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

Almost Contact Metric ◽

AbstractThe 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.

Pointwise slant submanifolds and their warped products in Sasakian manifolds

Filomat ◽

10.2298/fil1812131u ◽

2018 ◽

Vol 32 (12) ◽

pp. 4131-4142 ◽

Cited By ~ 2

Author(s):

Siraj Uddin ◽

Ali Alkhaldi

Keyword(s):

Warped Product ◽

Warped Products ◽

Sasakian Manifolds ◽

Slant Submanifolds ◽

Hermitian Manifolds ◽

Almost Hermitian Manifolds ◽

Almost Contact Metric ◽

Recently, B.-Y. Chen and O.J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. In this paper, first we study pointwise slant and pointwise pseudo-slant submanifolds of almost contact metric manifolds and then using this notion, we show that there exist a non-trivial class of warped product pointwise pseudo-slant submanifolds of Sasakian manifolds by giving some useful results, including a characterization.

Pointwise Slant and Pointwise Semi-Slant Submanifolds in Almost Contact Metric Manifolds

Mathematics ◽

10.3390/math8060985 ◽

2020 ◽

Vol 8 (6) ◽

pp. 985

Author(s):

Kwang Soon Park

Keyword(s):

Fundamental Form ◽

Second Fundamental Form ◽

Warping Function ◽

Topological Properties ◽

Slant Submanifolds ◽

Kenmotsu Manifolds ◽

Almost Contact Metric ◽

In almost contact metric manifolds, we consider two kinds of submanifolds: pointwise slant, pointwise semi-slant. On these submanifolds of cosymplectic, Sasakian and Kenmotsu manifolds, we obtain characterizations and study their topological properties and distributions. We also give their examples. In particular, we obtain some inequalities consisting of a second fundamental form, a warping function and a semi-slant function.

Semi-invariant ξ⊥-Riemannian submersions from almost contact metric manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500748 ◽

2017 ◽

Vol 14 (05) ◽

pp. 1750074 ◽

Cited By ~ 4

Author(s):

Mehmet Akif Akyol ◽

Ramazan Sarı ◽

Elif Aksoy

Keyword(s):

Riemannian Manifolds ◽

Riemannian Submersion ◽

Necessary And Sufficient Condition ◽

Sasakian Manifolds ◽

Riemannian Submersions ◽

Almost Contact Metric ◽

Definition Of ◽

Necessary And Sufficient ◽

As a generalization of anti-invariant [Formula: see text]-Riemannian submersions, we introduce semi-invariant [Formula: see text]-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant [Formula: see text]-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant [Formula: see text]-Riemannian submersions with totally umbilical fibers.

Almost Contact Metric Manifolds with Local Riemannian and Ricci Symmetries

Mediterranean Journal of Mathematics ◽

10.1007/s00009-019-1362-6 ◽

2019 ◽

Vol 16 (4) ◽

Cited By ~ 1

Author(s):

Yaning Wang

Keyword(s):

Almost Contact Metric ◽

D-Homothetic Deformation of Normal Almost Contact Metric Manifolds

Ukrainian Mathematical Journal ◽

10.1007/s11253-013-0732-7 ◽

2013 ◽

Vol 64 (10) ◽

pp. 1514-1530 ◽

Cited By ~ 4

Author(s):

U. C. De ◽

S. Ghosh

Keyword(s):

Almost Contact Metric ◽

Lifting semi-invariant submanifolds to distribution of almost contact metric manifolds

Differential Geometry of Manifolds of Figures ◽

10.5922/0321-4796-2020-51-5 ◽

2020 ◽

pp. 39-48

Author(s):

A. V. Bukusheva

Keyword(s):

Parallel Transport ◽

Linear Connection ◽

Contact Metric Manifold ◽

Almost Contact Metric Structure ◽

Almost Contact Metric Manifold ◽

Almost Contact Metric ◽

Invariant Submanifolds ◽

Contact Metric Structure ◽

Let M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the interior connection that allows parallel transport of admissible vectors along admissible curves. The assigment of the linear connection is equivalent to the assignment of a Riemannian metric of the Sasaki type on the distribution D. Certain tensor field of type (1,1) on D defines a so-called prolonged almost contact metric structure. Each section of the distribution D defines a morphism of smooth manifolds. It is proved that if a semi-invariant submanifold of the manifold M and is a covariantly constant vector field with respect to the N-connection , then is a semi-invariant submanifold of the manifold D with respect to the prolonged almost contact metric structure.