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Scalar curvature of QR-submanifolds with maximal QR-dimension in a quaternionic projective space

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Abstract

In this paper we derive an integral formula on an n-dimensional, compact, minimal QR-submanifoldM of (p−1) QR-dimension immersed in a quaternionic projective space QP (n+p)/4. 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 tube over a quaternionic projective space.

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Author information

Correspondence to Hyang Sook Kim.

Additional information

This work was supported by the 2010 Inje University research grant.

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Kim, H.S., Pak, J.S. Scalar curvature of QR-submanifolds with maximal QR-dimension in a quaternionic projective space. Indian J Pure Appl Math 42, 109 (2011). https://doi.org/10.1007/s13226-011-0007-7

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Key words

  • quaternionic projective space
  • scalar curvature
  • QR-submanifold
  • maximal QR-dimension
  • quaternionic invariant distribution
  • minimal