Abstract
Extremities Involving B. Y. Chen’s Invariants for Real Hypersurfaces in Complex Quadric
Highlights
Afterwards, many papers have been appeared in submanifolds of space forms in the version of real and complex like, generalised complex space forms [11], (k, μ)-contact space forms [1] and Sasakian space forms [13]
The classifications of real hypersurface of the complex quadric with isometric Reeb flow were obtained by Berndt and Suh [5] and many more work have been studied by different authors considering the same ambient space ([2]-[4],[19])
We establish an inequality in terms of the warping function and the scalar curvature for warped product real hypersurface of Qm and some obstructions have been given
Summary
Chen found some obstructions to Chern’s problem and proposed inequalities for submanifolds in Riemannian space form concerning the sectional curvature, the scalar curvature and the squared mean curvature [9]. J. Suh, obtained some analyzing results on real hypersurfaces in the complex quadric by considering some geometric conditions like parallel Ricci tensor [17], Reeb parallel shape operator [18]. The classifications of real hypersurface of the complex quadric with isometric Reeb flow were obtained by Berndt and Suh [5] and many more work have been studied by different authors considering the same ambient space ([2]-[4],[19]). We first establish Chen’s extremities for real hypersurfaces of the complex quadric Qm and considering the equality case, we obtain some consequences. By virtue of simpleness, throughout a paper we denote semi-symmetric metric connection, LeviCivita connection and Warped product by SSMC, LC connection and WP, respectively
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