no. 9-10
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

Shahid, Mohammad Hasan1 ; Al-Solamy, Falleh R.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, Tome 349 (2011) no. 9-10, pp. 571-573.

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 QPm(4c) in terms of the main extrinsic invariant, namely the square mean curvature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.013
Shahid, Mohammad Hasan 1 ; Al-Solamy, Falleh R. 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 
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Shahid, Mohammad Hasan; Al-Solamy, Falleh R. Ricci tensor of slant submanifolds in a quaternion projective space. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 571-573. doi : 10.1016/j.crma.2011.01.013. http://www.numdam.org/articles/10.1016/j.crma.2011.01.013/

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

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

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