PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn


MURATHAN C., ÖZGÜR C.

GLASGOW MATHEMATICAL JOURNAL, vol.51, pp.331-339, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51
  • Publication Date: 2009
  • Doi Number: 10.1017/s001708950900500x
  • Journal Name: GLASGOW MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.331-339
  • Bursa Uludag University Affiliated: Yes

Abstract

Let M be an n-dimensional totally real minimal submanifold in CPn. We prove that if M is semi-parallel and the scalar curvature tau, -(n-1)(n-2)(n+1)/2 <= tau <= 0, then M is an open part of the Clifford torus T-n subset of CPn. If M is semi-parallel and the scalar curvature tau, n(n - 1) <= tau <= n(3)-3n+2/2, then M is an open part of the real projective space RPn.