Search results
1 – 6 of 6In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for…
Abstract
In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, the equality case is also discussed. By the application of derived inequality, we compute an expression for Dirichlet energy of the involved warping function. Finally, we also proved some classifications for these warped product submanifolds in terms of Ricci solitons and Ricci curvature. A non-trivial example of these warped product submanifolds is provided.
Details
Keywords
H. Aruna Kumara, V. Venkatesha and Devaraja Mallesha Naik
Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance…
Abstract
Purpose
Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds.
Design/methodology/approach
The paper opted the tensor calculus on manifolds to find the solution of the CPE.
Findings
In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting.
Originality/value
The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.
Details
Keywords
Mohd Danish Siddiqi, Sudhakar Kumar Chaubey and Aliya Naaz Siddiqui
The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance…
Abstract
Purpose
The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.
Design/methodology/approach
This research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples.
Findings
The major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds.
Originality/value
The results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided.
Details
Keywords
Sudhakar Kumar Chaubey and Uday Chand De
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the…
Abstract
Purpose
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly
Design/methodology/approach
The authors have used the tensorial approach to achieve the goal.
Findings
A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.
Originality/value
The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.
Details
Keywords
Siraj Uddin, Ion Mihai and Adela Mihai
Chen (2001) initiated the study of CR-warped product submanifolds in Kaehler manifolds and established a general inequality between an intrinsic invariant (the warping function…
Abstract
Chen (2001) initiated the study of CR-warped product submanifolds in Kaehler manifolds and established a general inequality between an intrinsic invariant (the warping function) and an extrinsic invariant (second fundamental form).
In this paper, we establish a relationship for the squared norm of the second fundamental form (an extrinsic invariant) of warped product bi-slant submanifolds of Kenmotsu manifolds in terms of the warping function (an intrinsic invariant) and bi-slant angles. The equality case is also considered. Some applications of derived inequality are given.
Details
Keywords
Aykut Akgün and Mehmet Gülbahar
Bi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.
Abstract
Purpose
Bi-slant submanifolds of S-manifolds are introduced, and some examples of these submanifolds are presented.
Design/methodology/approach
Some properties of Di-geodesic and Di-umbilical bi-slant submanifolds are examined.
Findings
The Riemannian curvature invariants of these submanifolds are computed, and some results are discussed with the help of these invariants.
Originality/value
The topic is original, and the manuscript has not been submitted to any other journal.
Details