Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds

Olteanu, Andreea

doi:10.36890/iejg.545055

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Olteanu also showed in Reference [63] that the same result holds for an antiinvariant doubly warped product f 2 N 1 × f 1 N 2 in a generalized Sasakian space form such that the Reeb vector field ξ is normal to f 2 N 1 × f 1 N 2 . In Reference [64], she obtained similar inequalities for doubly warped products isometrically immersed into locally conformal almost cosymplectic manifolds. In addition, in Reference [65], she derived similar inequalities for doubly warped products isometrically immersed into S-space forms.…”

Section: Doubly Warped Product Submanifoldsmentioning

confidence: 88%

Geometric Inequalities for Warped Products in Riemannian Manifolds

Chen

Blaga

2021

Mathematics

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Warped products are the most natural and fruitful generalization of Riemannian products. Such products play very important roles in differential geometry and in general relativity. After Bishop and O’Neill’s 1969 article, there have been many works done on warped products from intrinsic point of view during the last fifty years. In contrast, the study of warped products from extrinsic point of view was initiated around the beginning of this century by the first author in a series of his articles. In particular, he established an optimal inequality for an isometric immersion of a warped product N1×fN2 into any Riemannian manifold Rm(c) of constant sectional curvature c which involves the Laplacian of the warping function f and the squared mean curvature H2 . Since then, the study of warped product submanifolds became an active research subject, and many papers have been published by various geometers. The purpose of this article is to provide a comprehensive survey on the study of warped product submanifolds which are closely related with this inequality, done during the last two decades.

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Section: Doubly Warped Product Submanifoldsmentioning

confidence: 88%

Geometric Inequalities for Warped Products in Riemannian Manifolds

Chen

Blaga

2021

Mathematics

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“…The research conducted by Chen has sparked the interest of geometers, resulting in the derivation of several geometric inequalities for warped products and doubly warped products [4][5][6][7][8][9][10][11][12][13][14]. These investigations have taken place in different scenarios, incorporating various ambient manifolds [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Pinching Results for Doubly Warped Products’ Pointwise Bi-Slant Submanifolds in Locally Conformal Almost Cosymplectic Manifolds with a Quarter-Symmetric Connection

Aquib,

Al-Dayel,

Aslam

et al. 2024

Symmetry

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In this research paper, we establish geometric inequalities that characterize the relationship between the squared mean curvature and the warping functions of a doubly warped product pointwise bi-slant submanifold. Our investigation takes place in the context of locally conformal almost cosymplectic manifolds, which are equipped with a quarter-symmetric metric connection. We also consider the cases of equality in these inequalities. Additionally, we derive some geometric applications of our obtained results.

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Doubly Warped Products in Locally Conformal Almost Cosymplectic Manifolds

Cited by 2 publications

References 11 publications

Geometric Inequalities for Warped Products in Riemannian Manifolds

Geometric Inequalities for Warped Products in Riemannian Manifolds

Pinching Results for Doubly Warped Products’ Pointwise Bi-Slant Submanifolds in Locally Conformal Almost Cosymplectic Manifolds with a Quarter-Symmetric Connection

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