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SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE

박진석|김향숙
대한수학회 (The Korean Mathematical Society)|2010.05|대한수학회보 (Bulletin of the KMS)|제47권 제3호|pp. 541-549

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참고문헌

키워드

Sasakian manifoldscalar curvaturecontact CR-submanifoldodd-dimensional unit sphere
주제분류수학

초록

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n − 1)contact CR-dimension immersed in a unit (2m+1)-sphere S2m+1. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

Abstract

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n − 1)contact CR-dimension immersed in a unit (2m+1)-sphere S2m+1. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

참고문헌 (12)

  1. A. Bejancu, "Geometry of CR-Submanifolds" (1886), D. Reidel Publishing Company
  2. B. Y. Chen, "Geometry of Submanifolds" (1973), Marcel Dekker Inc.
  3. M. Djorić, "The scalar curvature of CR submanifolds of maximal CR dimension of complex projective space", Monatsh. Math., 154(1), pp.11~17 (2008)
  4. J. Erbacher, "Reduction of the codimension of an isometric immersion", J. Differential Geometry, 5, pp.333~340 (1971)
  5. 김향숙, "Certain contact $CR$-submanifolds of an odd-dimensional unit sphere", 대한수학회보, 44(1), pp.109~116 (2007), 대한수학회
  6. H. S. Kim, "Certain class of contact CR-submanifolds of an odd-dimensional unit sphere", Taiwanese Math. J.
  7. H. S. Kim, "Scalar curvature of QR-submanifolds with maximal QR-dimension in a quaternionic projective space, submitted", ~
  8. M. Kon, "On hypersurfaces immersed in S2n+1", Ann. Fac. Sci. Univ. Nat. Zaïre (Kinshasa) Sect. Math.-Phys., 4(1), pp.1~24 (1978)
  9. J.-H. Kwon, "On some contact CR-submanifolds of an odd-dimensional unit sphere", Soochow J. Math., 26(4), pp.427~439 (2000)
  10. J. S. Pak, "Contact CR-submanifolds of an odd-dimensional unit sphere", Geom. Dedicata, 114, pp.1~11 (2005)
  11. K. Yano, "Integral Formulas in Riemannian Geometry" (1970), Marcel Dekker, Inc.
  12. K. Yano, "CR Submanifolds of Kaehlerian and Sasakian Manifolds" (1983), Birkhauser

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