Motor cortex excitability during spine shape-judgment in adolescent idiopathic scoliosis: a TMS motor evoked potential study. [PDF]
Exp Brain ResVirovec M, Barumerli R, Cesari P.
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Shape and Scale in Quantifying Aortic Morphology Evolution and Chronicity. [PDF]
Cardiovasc Eng TechnolPugar JA, Jiang D, Kim J, Pocivavsek L.
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The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature. [PDF]
PLoS Comput BiolKhabaz K +16 more
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In this paper, we establish Casorati inequalities for Riemannian maps and Riemannian submersions involving quaternionic space forms, and we provide geometric characterisations of their equality cases. First, we derive Casorati inequalities for Riemannian maps to quaternionic space forms and describe the corresponding equality cases, showing that the ...
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Inequalities for the Casorati Curvatures of Slant Submanifolds in Quaternionic Space Forms [PDF]
Journal of Inequalities and Applications, 2014 Abstract In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.
Gabriel-Eduard Vilcu +2 more
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Optimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed With Semi-Symmetric Non-Metric Connections [PDF]
Symmetry, 2016 In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection.
Hairong Liu, Guoqing He
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Inequalities for the Casorati Curvatures of Real Hypersurfaces in Some Grassmannians
Taiwanese Journal of Mathematics, 2018 In this paper we obtain two types of optimal inequalities consisting of the normalized scalar curvature and the generalized normalized $δ$-Casorati curvatures for real hypersurfaces of complex two-plane Grassmannians and complex hyperbolic two-plane Grassmannians. We also find the conditions on which the equalities hold.
Kwang-Soon Park
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Inequalities for Casorati Curvatures of Submanifolds in Real Space Forms [PDF]
Advances in Geometry, 2016 Abstract Using Oprea’s optimization methods on submanifolds, we give another proof of the inequalities relating the normalized δ-Casoraticurvature δ ^
Zhang, Pan, Zhang, Liang
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Inequalities for Riemannian Submersions Involving Casorati Curvatures: A New Approach
6th International Students Science Congress Proceedings Book, 2022For 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 +2 more
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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 +3 more
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