Results 121 to 130 of about 469 (136)

Inequalities for Riemannian Submersions Involving Casorati Curvatures: A New Approach

6th International Students Science Congress Proceedings Book, 2022
For surfaces in a Euclidean 3-space Casorati [4] introduced a new curvature in 1890 what is today called the Casorati curvature. This curvature was preferred by Casorati over Gauss curvature because Gauss curvature may vanish for surfaces that look intuitively curved, while Casorati curvature only vanishes at the planer points. The Casorati curvature
Gülistan Polat, Bayram Şahin, Jae Won Lee   +2 more
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Inequalities for Algebraic Casorati Curvatures and Their Applications II

2017
Different kind of algebraic Casorati curvatures are introduced. A result expressing basic Casorati inequalities for algebraic Casorati curvatures is presented and equality cases are discussed. As their applications, basic Casorati inequalities for different \(\delta \)-Casorati curvatures for different kind of submanifolds of quaternionic space forms ...
Young Jin Suh, Mukut Mani Tripathi
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Optimal inequalities for the normalizedδ-Casorati curvatures of submanifolds in Kenmotsu space forms

Advances in Geometry, 2017
AbstractIn this paper, we establish two sharp inequalities for the normalizedδ-Casorati curvatures of submanifolds in a Kenmotsu space form, tangent to the structure vector field of the ambient space.Moreover, we show that in both cases the equality at all points characterizes the totally geodesic submanifolds.
Lee, Chul Woo, Lee, Jae Won, Vîlcu, Gabriel-Eduard   +2 more
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Certain inequalities for the Casorati curvatures of submanifolds of generalized (k,μ)-space-forms

Asian-European Journal of Mathematics, 2018
The paper deals with the study of Casorati curvature of submanifolds of generalized [Formula: see text]-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.
Hui, Shyamal Kumar, Mandal, Pradip, Alkhaldi, Ali H., Pal, Tanumoy   +3 more
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Optimization Approach for Bounds Involving Generalized Normalized $$\delta $$ -Casorati Curvatures

2018
By using T. Oprea’s optimization method on a real hypersurfaces of complex quadric \(Q^{m}\) with QSMC, we prove extremal inequalities concerning normalized scalar curvature and generalized normalized \(\delta \)-Casorati curvatures. Moreover, we show the equilibrium cases at all points which signalize the invariantly quasi-umbilical real hypersurfaces.
Pooja Bansal, Mohammad Hasan Shahid
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Some bounds for Casorati curvatures on Golden Riemannian space forms with SSM connection

2022
In this article, we derive some sharp inequalities for slant submanifolds immersed into golden Riemannian space forms with a semi-symmetric metric connection. Also, we characterize submanifolds for the case of equalities. Lastly, we discuss these inequalities for some special submanifolds.
Lee, Jae Won, Choudhary, Majid Ali, Sıddıquı, Aliya Naaz   +2 more
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A Geometric Interpretation of Cauchy-Schwarz Inequality in Terms of Casorati Curvature

2017
In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribedcurvature conditions to the admissible maximal length of geodesics on a surface. Bonnet’s workopened the pathway for the quest of further connections between curvature conditions andother geometric properties of surfaces, hypersurfaces or Riemannian ...
BRUBAKER, Nicholas D., SUCEAVA, Bogdan D.   +1 more
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Optimal inequalities involving Casorati curvatures along Riemannian maps and Riemannian submersions for Sasakian space forms

Journal of Geometry and Physics
The paper establishes some optimal inequalities for Casorati curvatures in the setting of Sasakian space forms, focusing on two important types of smooth maps between Riemannian manifolds: Riemannian maps and Riemannian submersions. Riemannian maps generalize both isometric immersions and Riemannian submersions by relaxing the conditions on how the ...
Gülistan Polat, Jae Won Lee, Bayram Şahin   +2 more
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Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

Entropy, 2022
Simona Decu, Gabriel-Eduard Vîlcu
exaly  

Estimates of B.-Y. Chen’s δˆ-Invariant in Terms of Casorati Curvature and Mean Curvature for Strictly Convex Euclidean Hypersurfaces

2018
B.-Y. Chen’s δˆ-invariants can be estimated in function of other curvature terms through an algebraicprocess using the AM-GM and AM-QM inequalities. This procedure works on strictly convexsmooth hypersurfaces lying in an Euclidean ambient space, and the estimates relate some  δˆ-invariants to Germain’s mean curvature and ...
Suceava, Bogdan D., Vajiac, Mihaela
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