Ricci tensor of slant submanifolds in a quaternion projective space

Mohammad Hasan Shahid; Falleh R. Al-Solamy

doi:10.1016/j.crma.2011.01.013

Differential Geometry

Ricci tensor of slant submanifolds in a quaternion projective space
[Tenseur de Ricci dʼune sous-variété oblique M dans un espace projectif quaternionien]

Présenté par : Jean-Michel Bismut

Mohammad Hasan Shahid ¹ ; Falleh R. Al-Solamy ²

¹ Department of Mathematics, Faculty of Natural Science, Jamia Millia Islamia, New Delhi-110025, India
² Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 80015, Jeddah 21589, Saudi Arabia

Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 571-573.

Résumé
Abstract

Nous définissons et étudions des sous-variétés obliques dʼune variété Kahlerienne quaternionienne et plus particuliérement dʼun espace projectif quaternionien. Nous obtenons une estimation fine du tenseur de Ricci dʼune sous-variété oblique M dans un espace projectif quaternionien, en termes de lʼinvariant extrinsèque principal, à savoir la courbure moyenne quadratique.

We study slant submanifolds of quaternion Kaehler manifold and in particular of a quaternion projective space. We obtain a sharp estimate of the Ricci tensor of a slant submanifold M in a quaternion projective space ${QP}^{m} (4 c)$ in terms of the main extrinsic invariant, namely the square mean curvature.

Reçu le : 2009-09-01
Accepté le : 2011-01-06
Publié le : 2011-04-30

DOI : 10.1016/j.crma.2011.01.013

Affiliations des auteurs :

Mohammad Hasan Shahid ¹ ; Falleh R. Al-Solamy ²

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     author = {Mohammad Hasan Shahid and Falleh R. Al-Solamy},
     title = {Ricci tensor of slant submanifolds in a quaternion projective space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {571--573},
     publisher = {Elsevier},
     volume = {349},
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     year = {2011},
     doi = {10.1016/j.crma.2011.01.013},
     language = {en},
}

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Mohammad Hasan Shahid; Falleh R. Al-Solamy. Ricci tensor of slant submanifolds in a quaternion projective space. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 571-573. doi : 10.1016/j.crma.2011.01.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.013/

Bibliographie
Cité par

[1] B.Y. Chen Geometry of Slant Submanifolds, K.U. Leuven, 1990

[2] B.Y. Chen A General inequality for submanifolds in complex space forms and its application, Arch. Math., Volume 67 (1996), pp. 519-528

[3] B.Y. Chen; Y. Tazawa Slant submanifolds of complex projective and complex hyperbolic spaces, Glasg. Math. J., Volume 42 (2000), pp. 439-454

[4] S. Ishihara Quaternion Kaehler manifolds, J. Differential Geom., Volume 9 (1974), pp. 483-500

[5] B. Sahin Slant submanifolds of quaternion Kaehler manifolds, Commun. Korean Math. Soc., Volume 22 (2007) no. 1, pp. 123-135

[6] Liu Ximin On Ricci curvature of totally real submanifolds in a quaternion projective space, Arch. Math. (Brno), Volume 38 (2002), pp. 297-305

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