Bounds for generalized normalized δ-Casorati curvatures for submanifolds in Bochner Kaehler manifold

In this paper, we prove sharp inequalities between the normalized scalar curvature and the generalized normalized ?-Casorati curvatures for different submanifolds in Bochner Kaehler manifold. Moreover, We also characterize submanifolds on which the equalities hold.

Some inequalities of slant submanifolds in generalized complex space forms

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.36.2005.114 ◽

2005 ◽

Vol 36 (3) ◽

pp. 223-229 ◽

Cited By ~ 1

Author(s):

Aimin Song ◽

Ximin Liu

Keyword(s):

Scalar Curvature ◽

Ricci Curvature ◽

Mean Curvature ◽

Complex Space ◽

Space Forms ◽

Slant Submanifolds ◽

Generalized Complex ◽

Complex Space Forms ◽

In this paper, we obtain an inequality about Ricci curvature and squared mean curvature of slant submanifolds in generalized complex space forms. We also obtain an inequality about the squared mean curvature and the normalized scalar curvature of slant submanifolds in generalized coplex space forms.

Lower Bounds on Statistical Submersions with vertical Casorati curvatures

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988782250044x ◽

2021 ◽

Author(s):

Aliya Naaz Siddiqui ◽

Mohd Danish Siddiqi ◽

Ali H. Alkhaldi ◽

Akram Ali

Keyword(s):

Scalar Curvature ◽

Lower Bounds ◽

Statistical Manifolds ◽

Statistical Submersion

In this paper, we obtain lower bounds for the normalized scalar curvature on statistical submersion with the normalized [Formula: see text]-vertical Casorati curvatures. Also, we discuss the conditions for which the equality cases hold. Beside this, we determine the statistical solitons on statistical submersion from statistical manifolds and illustrate an example of statistical submersions from statistical manifolds.

Complex submanifolds with constant scalar curvature in a Kaehler manifold

Journal of the Mathematical Society of Japan ◽

10.2969/jmsj/02710076 ◽

1975 ◽

Vol 27 (1) ◽

pp. 76-81 ◽

Cited By ~ 4

Author(s):

Masahiro KON

Keyword(s):

Scalar Curvature ◽

Constant Scalar Curvature ◽

Kaehler Manifold ◽

Complex Submanifolds

A lower bound of normalized scalar curvature for the submanifolds of locally conformal Kaehler space form using Casorati curvatures

Filomat ◽

10.2298/fil1715925l ◽

2017 ◽

Vol 31 (15) ◽

pp. 4925-4932 ◽

Cited By ~ 2

Author(s):

Mehraj Lone

Keyword(s):

Lower Bound ◽

Scalar Curvature ◽

Space Form ◽

Equality Case ◽

Locally Conformal ◽

In the present paper, we prove the inequality between the normalized scalar curvature and the generalized normalized ?-Casorati curvatures for the submanifolds of locally conformal Kaehler space form and also consider the equality case of the inequality.

GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887810004403 ◽

2010 ◽

Vol 07 (03) ◽

pp. 505-515 ◽

Cited By ~ 7

Author(s):

M. BROZOS-VÁZQUEZ ◽

P. GILKEY ◽

E. MERINO

Keyword(s):

Scalar Curvature ◽

Curvature Tensor ◽

Constant Scalar Curvature ◽

Kaehler Manifold ◽

Algebraic Curvature Tensor ◽

Algebraic Curvature

We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar curvature.

Optimal casorati inequalities on bi-slant submanifolds of generalized sasakian space forms

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.49.2018.2638 ◽

2018 ◽

Vol 49 (3) ◽

pp. 235-255 ◽

Cited By ~ 1

Author(s):

Aliya Naaz Siddiqui

Keyword(s):

Scalar Curvature ◽

Optimization Method ◽

Space Forms ◽

Slant Submanifolds ◽

Sasakian Space Forms ◽

In this paper, we use T Oprea's optimization method to establish some optimal Casorati inequalities, which involve the normalized scalar curvature for bi-slant submanifolds of generalized Sasakian space forms. In the continuation, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical.

Bounds for generalized normalized δ-Casorati curvatures for Bi-slant submanifolds in T-space forms

Filomat ◽

10.2298/fil1801329a ◽

2018 ◽

Vol 32 (1) ◽

pp. 329-340 ◽

Cited By ~ 3

Author(s):

Mohd. Aquib

Keyword(s):

Scalar Curvature ◽

Space Forms ◽

Equality Case ◽

Slant Submanifolds ◽

Invariant Submanifolds ◽

Cr Submanifolds

In this paper, we prove the inequality between the generalized normalized ?-Casorati curvatures and the normalized scalar curvature for the bi-slant submanifolds in T-space forms and consider the equality case of the inequality. We also develop same results for semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds, slant submanifolds, invariant and anti-invariant submanifolds in T-space forms.

Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds

Mathematics ◽

10.3390/math10020176 ◽

2022 ◽

Vol 10 (2) ◽

pp. 176

Author(s):

Aliya Naaz Siddiqui ◽

Mohd Danish Siddiqi ◽

Ali Hussain Alkhaldi

Keyword(s):

Scalar Curvature ◽

Fundamental Form ◽

Second Fundamental Form ◽

The Second Fundamental Form ◽

Statistical Manifolds ◽

Equality Condition ◽

Legendrian Submanifolds

In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical manifolds containing the normalized scalar curvature and the generalized normalized Casorati curvatures. We also define the second fundamental form of those submanifolds that satisfy the equality condition. On Legendrian submanifolds of Kenmotsu-like statistical manifolds, we discuss a conjecture for Wintgen inequality. At the end, some immediate geometric consequences are stated.

Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures

Mathematics ◽

10.3390/math6110259 ◽

2018 ◽

Vol 6 (11) ◽

pp. 259 ◽

Cited By ~ 2

Author(s):

Chul Lee ◽

Jae Lee

Keyword(s):

Scalar Curvature ◽

Riemannian Metric ◽

Statistical Manifold ◽

Statistical Structure ◽

Slant Submanifolds ◽

Statistical Manifolds ◽

Conjugate Connections ◽

Levi Civita Connection ◽

Totally Real

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ∇ * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant φ -sectional curvature. In addition, we give examples to show that the total space is a sphere.

Pinching Theorems for a Vanishing C-Bochner Curvature Tensor

Mathematics ◽

10.3390/math6110231 ◽

2018 ◽

Vol 6 (11) ◽

pp. 231

Author(s):

Jae Lee ◽

Chul Lee

Keyword(s):

Scalar Curvature ◽

Curvature Tensor ◽

Sasakian Manifold ◽

Bochner Tensor ◽

Casorati Curvature

The main purpose of this article is to construct inequalities between a main intrinsic invariant (the normalized scalar curvature) and an extrinsic invariant (the Casorati curvature) for some submanifolds in a Sasakian manifold with a zero C-Bochner tensor.