scholarly journals On locally conformal Kaehler space forms

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 593-597
Author(s):  
Pegah Mutlu ◽  
Zerrin Sentürk
Keyword(s):  
Curvature Tensor ◽  
Space Form ◽  
Hermitian Manifold ◽  
Kaehler Manifold ◽  
Space Forms ◽  
Holomorphic Curvature ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Locally Conformal

The notion of a locally conformal Kaehler manifold (an l.c.K-manifold) in a Hermitian manifold has been introduced by I. Vaisman in 1976. In [2], K. Matsumoto introduced some results with the tensor Pij is hybrid. In this work, we give a generalisation about the results of an l.c.K-space form with the tensor Pij is not hybrid. Moreover, the Sato?s form of the holomorphic curvature tensor in almost Hermitian manifolds and l.c.K-manifolds are presented.

scholarly journals Warped product semi-slant submanifolds in locally conformal Kaehler manifolds II

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Warped Product ◽  
Space Form ◽  
Sufficient Conditions ◽  
Hermitian Manifold ◽  
Second Fundamental Form ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Locally Conformal

In 1994 N.~Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of $CR$- and slant-submanifolds, \cite{MR0353212}, \cite{MR760392}. In particular, he considered this submanifold in Kaehlerian manifolds, \cite{MR1328947}. Then, in 2007, V.~A.~Khan and M.~A.~Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, \cite{MR2364904}. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and we gave a necessary and sufficient conditions of the two distributions (holomorphic and slant) be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form. In the last paper, we defined $2$-kind warped product semi-slant submanifolds in almost hermitian manifolds and studied the first kind submanifold in a locally conformal Kaehler manifold. Using Gauss equation, we derived some properties of this submanifold in an locally conformal Kaehler space form, \cite{MR2077697}, \cite{MR3728534}. In this paper, we consider same submanifold with the parallel second fundamental form in a locally conformal Kaehler space form. Using Codazzi equation, we partially determine the tensor field $P$ which defined in~\eqref{1.3}, see Theorem~\ref{th4.1}. Finally, we show that, in the first type warped product semi-slant submanifold in a locally conformal space form, if it is normally flat, then the shape operators $A$ satisfy some special equations, see Theorem~\ref{th5.2}.

scholarly journals A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds

2016 ◽  
Vol 47 (2) ◽  
pp. 143-161 ◽  
Author(s):  
Mehmet Gulbahar ◽  
Erol Kilic ◽  
Sadik Keles
Keyword(s):  
Orthonormal Basis ◽  
Complex Space ◽  
Space Form ◽  
Hermitian Manifold ◽  
Complex Space Form ◽  
Slant Submanifold ◽  
Almost Hermitian Manifold ◽  
Slant Submanifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.

scholarly journals ANTI-INVARIANT RIEMANNIAN SUBMERSIONS FROM LOCALLY CONFORMAL KAEHLER MANIFOLDS

2021 ◽  
pp. 1031
Author(s):  
Majid Ali Choudhary ◽  
Lamia Saeed Alqahtani
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Locally Conformal

Recently, Sahin [10] studied the anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In present work, these notions of anti-invariant and Lagrangian Riemannian submersions have been extended to locally conformal Kaehler manifolds. Certain decomposition results and the geometry of foliation have also been investigated.

scholarly journals QUASI-CONFORMAL CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS

2020 ◽  
Vol 35 (1) ◽  
pp. 089
Author(s):  
Braj B. Chaturvedi ◽  
Brijesh K. Gupta
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Space Form ◽  
Riemannian Curvature ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Riemannian Curvature Tensor

The present paper deals the study of generalised Sasakian-space-forms with the conditions Cq(ξ,X).S = 0, Cq(ξ,X).R = 0 and Cq(ξ,X).Cq = 0, where R, S and Cq denote Riemannian curvature tensor, Ricci tensor and quasi-conformal curvature tensor of the space-form, respectively and at last, we have given some examples to improve our results.

scholarly journals On locally conformal Kähler space forms

1985 ◽  
Vol 8 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Covariant Differentiation ◽  
Space Forms ◽  
Riemannian Curvature Tensor ◽  
Locally Conformal Kähler ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Lee Form

Anm-dimensional locally conformal Kähler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closedl-formαλ(called the Lee form) whose structure(Fμλ,gμλ)satisfies∇νFμλ=−βμgνλ+βλgνμ−αμFνλ+αλFνμ, where∇λdenotes the covariant differentiation with respect to the Hermitian metricgμλ,βλ=−Fλϵαϵ,Fμλ=Fμϵgϵλand the indicesν,μ,…,λrun over the range1,2,…,m.For l. c. K-manifolds, I. Vaisman [4] gave a typical example and T. Kashiwada ([1], [2],[3]) gave a lot of interesting properties about such manifolds.In this paper, we shall study certain properties of l. c. K-space forms. In§2, we shall mainly get the necessary and sufficient condition that an l. c. K-space form is an Einstein one and the Riemannian curvature tensor with respect togμλwill be expressed without the tensor fieldPμλ. In§3, we shall get the necessary and sufficient condition that the length of the Lee form is constant and the sufficient condition that a compact l. c. K-space form becomes a complex space form. In the last§4, we shall prove that there does not exist a non-trivial recurrent l. c. K-space form.

scholarly journals On Kähler-like and G-Kähler-like almost Hermitian manifolds

2020 ◽  
Vol 7 (1) ◽  
pp. 145-161
Author(s):  
Masaya Kawamura
Keyword(s):  
Complex Structure ◽  
Hermitian Manifold ◽  
Almost Complex Structure ◽  
Almost Hermitian Manifold ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds ◽  
Balanced Metric

AbstractWe introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0, then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.

scholarly journals On generalized complex space forms satisfying certain curvature conditions

2016 ◽  
Vol 8 (2) ◽  
pp. 284-294
Author(s):  
M.M. Praveena ◽  
C.S. Bagewadi
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Complex Space ◽  
Space Form ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Space Forms ◽  
Generalized Complex ◽  
Curvature Tensors ◽  
Complex Space Forms

We study Ricci soliton $(g,V,\lambda)$ of generalized complex space forms when the Riemannian, Bochner and $W_{2}$ curvature tensors satisfy certain curvature conditions like semi-symmetric, Einstein semi-symmetric, Ricci pseudo symmetric and Ricci generalized pseudo symmetric. In this study it is shown that shrinking, steady and expansion of the generalized complex space forms depends on the solenoidal property of vector $V$. Also we prove that generalized complex space form with conservative Bochner curvature tensor is constant scalar curvature.

Sign in / Sign up

Export Citation Format

Share Document