Results 101 to 110 of about 277 (116)

Generalized normalized $$\varvec{\delta }$$ δ -Casorati curvature for statistical submanifolds in quaternion Kaehler-like statistical space forms

Journal of Geometry, 2018
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Aquib, Mohd., Shahid, Mohammad Hasan
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Lower Bounds on Statistical Submersions with vertical Casorati curvatures

International Journal of Geometric Methods in Modern Physics, 2021
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 ...
Aliya Naaz Siddiqui, Mohd Danish Siddiqi, Ali H. Alkhaldi, Akram Ali   +3 more
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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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On $$\delta $$-Casorati curvature invariants of Lagrangian submanifolds in quaternionic Kähler manifolds of constant q-sectional curvature

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023
This article is about \(\delta\)-Casorati curvature invariants of Lagrangian submanifolds of quaternionic space forms. Let us explain these terms one by one, in reverse order. Let \((M,g,\mathcal Q)\) be a quaternionic Kähler manifold, where \(\mathcal Q\subset \mathrm{End}\,(TM)\) is the quaternionic structure bundle.
Mohd Aquib, Mohamd Saleem Lone, Crina Neacşu, Gabriel-Eduard Vîlcu   +3 more
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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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