Titlebook: Geometry of Submanifolds and Applications; Bang-Yen Chen,Majid Ali Choudhary,Mohammad Nazrul Book 2024 The Editor(s) (if applicable) and

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,Conformal ,-Ricci-Yamabe Solitons in the Framework of Riemannian Manifolds, gradient CERYS . is an Einstein manifold and the gradient of smooth function . is a constant multiple of .. A non-trivial example of an . equipped with a semi-symmetric metric .-connection is constructed, and hence verify some of our results.

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,The Darboux Mate and the Higher Order Curvatures of Spherical Legendre Curves,, where . is the classical curvature function of .. Several examples are discussed, some of them in relationship with the usual theory of regular space curves. The case of Lorentz–Minkowski sphere . is sketched only from the point of view of the geodesic curvature.

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,Solitons in ,-Gravity,ent Yamabe solitons, .-Ricci and gradient .-Ricci solitons are its metrics. We establish criteria for which Ricci solitons are steady, expanding, or shrinking. Moreover, we study gradient Ricci solitons and prove that either the perfect fluid spacetime represents the dark energy era, or the spacetim

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,A Survey on Lagrangian Submanifolds of Nearly Kaehler Six-Sphere,rvey of results on Lagrangian submanifolds . of the nearly Kähler . in terms of a canonically induced almost contact metric structure, Chen’s equality, normal connection, normal curvature operator, Ricci tensor and conformal flatness. In particular, conditions for . to be Sasakian and totally geodes

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Pythagorean Submanifolds,odels of real space forms. They are defined by an equation based on the shape operator. We give several examples and observe that any Pythagorean submanifold is isoparametric where the principal curvatures are given in terms of the Golden ratio. We also classify Pythagorean hypersurfaces.

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