INEQUALITIES FOR GENERALIZED NORMALIZED $\delta$-CASORATI CURVATURES OF SLANT SUBMANIFOLDS IN QUATERNIONIC SPACE FORMS

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

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The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms

Mathematics ◽

10.3390/math7121151 ◽

2019 ◽

Vol 7 (12) ◽

pp. 1151 ◽

Cited By ~ 3

Author(s):

Mohd. Aquib ◽

Michel Nguiffo Boyom ◽

Mohammad Hasan Shahid ◽

Gabriel-Eduard Vîlcu

Keyword(s):

Complex Space ◽

Space Form ◽

Fundamental Equation ◽

Type Inequality ◽

Lagrangian Submanifold ◽

Space Forms ◽

Slant Submanifolds ◽

Sasakian Space Forms ◽

Generalized Complex ◽

Complex Space Forms

In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces.

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Chen’s δ-invariants type inequalities for bi-slant submanifolds in generalized Sasakian space forms

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2020.104040 ◽

2021 ◽

Vol 161 ◽

pp. 104040

Author(s):

Siraj Uddin ◽

Mohamd Saleem Lone ◽

Mehraj Ahmad Lone

Keyword(s):

Space Forms ◽

Slant Submanifolds ◽

Sasakian Space Forms

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Some inequalities of slant submanifolds in generalized complex space forms

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.36.2005.114 ◽

2005 ◽

Vol 36 (3) ◽

pp. 223-229 ◽

Cited By ~ 1

Author(s):

Aimin Song ◽

Ximin Liu

Keyword(s):

Scalar Curvature ◽

Ricci Curvature ◽

Mean Curvature ◽

Complex Space ◽

Space Forms ◽

Slant Submanifolds ◽

Generalized Complex ◽

Complex Space Forms ◽

Normalized Scalar Curvature

In this paper, we obtain an inequality about Ricci curvature and squared mean curvature of slant submanifolds in generalized complex space forms. We also obtain an inequality about the squared mean curvature and the normalized scalar curvature of slant submanifolds in generalized coplex space forms.

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B.Y. Chen inequalities for slant submanifolds in Sasakian space forms

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/bf02872761 ◽

2003 ◽

Vol 52 (3) ◽

pp. 367-381 ◽

Cited By ~ 2

Author(s):

Dragoş Cioroboiu ◽

Adela Oiagă

Keyword(s):

Space Forms ◽

Slant Submanifolds ◽

Sasakian Space Forms

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Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700003141 ◽

2003 ◽

Vol 74 (1) ◽

pp. 87-100

Author(s):

Setsuo Nagai

Keyword(s):

Projective Space ◽

Hyperbolic Space ◽

Real Hypersurfaces ◽

Quaternionic Projective Space ◽

Space Forms ◽

The Family ◽

Quaternionic Hyperbolic Space ◽

Quaternionic Space ◽

Naturally Reductive

AbstractWe determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).

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