Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Mihai, Adela; Iordache, Mihai

doi:10.3390/math6030044

Cited by 29 publications

(19 citation statements)

References 10 publications

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“…From 9, (11), and Theorem 2.1 [5] for the slant submanifold, it is not hard to come by the following:…”

Section: Warped Product Submanifolds Of the Form M ⊥ × F M θmentioning

confidence: 99%

“…Taking into account (7) for the nearly cosymplectic manifold, the virtues of (8), (11), and Theorem 2.1 in [5], it follows that:…”

Section: Lemmamentioning

confidence: 99%

“…The work of Chen is about the characterization of CR-warped products in Kaehler manifolds, and derives the inequality for the second fundamental form. In fact, distinct classes of warped product submanifolds of the different kinds of structures were studied by several geometers (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). Recently, Ali et al [15], established general inequalities for warped product pseudo-slants isometrically immersed in nearly Kenmotsu manifolds for mixed, totally geodesic submanifolds.…”

Section: Introductionmentioning

confidence: 99%

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The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

et al. 2019

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The aim of this paper is to construct a sharp general inequality for warped product pseudo-slant submanifold of the type M = M ⊥ × f M θ , in a nearly cosymplectic manifold, in terms of the warping function and the symmetric bilinear form h which is known as the second fundamental form. The equality cases are also discussed. As its application, we establish a bound for the first non-zero eigenvalue of the warping function whose base manifold is compact.

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“…From 9, (11), and Theorem 2.1 [5] for the slant submanifold, it is not hard to come by the following:…”

Section: Warped Product Submanifolds Of the Form M ⊥ × F M θmentioning

confidence: 99%

“…Taking into account (7) for the nearly cosymplectic manifold, the virtues of (8), (11), and Theorem 2.1 in [5], it follows that:…”

Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The First Eigenvalue Estimates of Warped Product Pseudo-Slant Submanifolds

et al. 2019

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“…These inequalities were extended by Aquib and Shahid [43] in the setting of statistical submanifolds in quaternion Kähler-like statistical space forms. On the other hand, Mihai et al [44] proved an Euler inequality and a Chen-Ricci inequality for statistical submanifolds of Hessian manifolds of constant Hessian curvature.…”

Section: Introductionmentioning

confidence: 99%

Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature

Decu

Haesen

Verstraelen

et al. 2018

Entropy

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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.

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“…Furthermore, in [4], Aydın et al found relations between the extrinsic and intrinsic invariants for submanifolds in statistical manifolds of constant curvature. In [16], Mihai and Mihai studied statistical submanifolds of Hessian manifolds of constant Hessian curvature. As generalizations of the results given in [4], the present authors studied the same problems for submanifolds in statistical manifolds of quasiconstant curvature [5].…”

Section: Introductionmentioning

confidence: 99%