Shahid, Mohammad Hasan; Al-Solamy, Falleh R. Ricci tensor of slant submanifolds in a quaternion projective space. (English) Zbl 1223.53043 C. R., Math., Acad. Sci. Paris 349, No. 9-10, 571-573 (2011). The authors prove the following: Suppose that \(M\) is an \(n\)-dimensional \(\theta\)-slant submanifold in a quaternion projective space \(\mathbb QP^m (4c)\), then, for each unit vector \(X\in T_p M,\) the Ricci tensor \(S(X)\) satisfies the inequality\[ S(X)\leq \tfrac{n^2}{4}\,H^2 +(n-1)c + 9c \cos ^2\theta. \]Equality holds identically for all unit tangent vectors at \(p\) if and only if \(p\) is a totally geodesic point or \(n=2\) and \(M\) is a totally umbilical point. Reviewer: Qilin Yang (Guangzhou) Cited in 6 Documents MSC: 53C40 Global submanifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:slant submanifold; quaternion projective space PDFBibTeX XMLCite \textit{M. H. Shahid} and \textit{F. R. Al-Solamy}, C. R., Math., Acad. Sci. Paris 349, No. 9--10, 571--573 (2011; Zbl 1223.53043) Full Text: DOI References: [1] Chen, B. Y., Geometry of Slant Submanifolds (1990), K.U. Leuven · Zbl 0716.53006 [2] Chen, B. Y., A General inequality for submanifolds in complex space forms and its application, Arch. Math., 67, 519-528 (1996) · Zbl 0871.53043 [3] Chen, B. Y.; Tazawa, Y., Slant submanifolds of complex projective and complex hyperbolic spaces, Glasg. Math. J., 42, 439-454 (2000) · Zbl 0979.53058 [4] Ishihara, S., Quaternion Kaehler manifolds, J. Differential Geom., 9, 483-500 (1974) · Zbl 0297.53014 [5] Sahin, B., Slant submanifolds of quaternion Kaehler manifolds, Commun. Korean Math. Soc., 22, 1, 123-135 (2007) · Zbl 1168.53313 [6] Ximin, Liu, On Ricci curvature of totally real submanifolds in a quaternion projective space, Arch. Math. (Brno), 38, 297-305 (2002) · Zbl 1090.53052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.