Skip to main content
SpringerLink
Log in

The scalar curvature of CR submanifolds of maximal CR dimension of complex projective space

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract.

We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • A Bejancu (1978) ArticleTitleCR-submanifolds of a Kähler manifold I Proc Amer Math Soc 69 135–142 Occurrence Handle0368.53040 Occurrence Handle10.2307/2043207 Occurrence Handle467630

    Article  MATH  MathSciNet  Google Scholar 

  • TE Cecil PJ Ryan (1982) ArticleTitleFocal sets and real hypersurfaces in complex projective space Trans Amer Math Soc 269 481–499 Occurrence Handle0492.53039 Occurrence Handle10.2307/1998460 Occurrence Handle637703

    Article  MATH  MathSciNet  Google Scholar 

  • YW Choe M Okumura (1997) ArticleTitleScalar curvature of a certain CR-submanifold of complex projective space Arch Math 68 340–346 Occurrence Handle0876.53037 Occurrence Handle10.1007/s000130050065 Occurrence Handle1435334

    Article  MATH  MathSciNet  Google Scholar 

  • Djorić M, Okumura M (2002) CR submanifolds of maximal CR dimension in complex manifolds. In: Oporda B et al (eds) PDE’s, Submanifolds and Affine Differential Geometry. Banach center publications 57: 89–99, Warsawa: Polish Academy of Sciences

  • HB Lawson SuffixJr (1970) ArticleTitleRigidity theorems in rank-1 symmetric spaces J Diff Geom 4 349–357 Occurrence Handle0199.56401 Occurrence Handle267492

    MATH  MathSciNet  Google Scholar 

  • R Nirenberg RO Wells SuffixJr (1965) ArticleTitleApproximation theorems on differentiable submanifolds of a complex manifold Trans Amer Math Soc 142 15–35 Occurrence Handle10.2307/1995342 Occurrence Handle245834

    Article  MathSciNet  Google Scholar 

  • M Okumura (1975) ArticleTitleOn some real hypersurfaces of a complex projective space Trans Amer Math Soc 212 355–364 Occurrence Handle0288.53043 Occurrence Handle10.2307/1998631 Occurrence Handle377787

    Article  MATH  MathSciNet  Google Scholar 

  • M Okumura (1989) ArticleTitleCodimension reduction problem for real submanifolds of complex projective space Colloq Math Soc János Bolyai 56 574–585

    Google Scholar 

  • AE Tumanov (1986) The geometry of CR manifolds Encyclopedia of Math Sci 9 VI, Several Complex Variables III Springer Berlin Heidelberg New York 201–221

    Google Scholar 

  • K Yano (1970) Integral Formulas in Riemannian Geometry Marcel Dekker New York Occurrence Handle0213.23801

    MATH  Google Scholar 

  • Yano K, Bochner S (1953) Curvature and Betti numbers. Ann Math Studies 32

Download references

Author information

Authors and Affiliations

  1. University of Belgrade, Belgrade, Serbia

    Mirjana Djorić

  2. Kawasaki, Japan

    Masafumi Okumura

Authors
  1. Mirjana Djorić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masafumi Okumura
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade, Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan

Rights and permissions

Reprints and permissions

About this article

Cite this article

Djorić, M., Okumura, M. The scalar curvature of CR submanifolds of maximal CR dimension of complex projective space. Monatsh Math 154, 11–17 (2008). https://doi.org/10.1007/s00605-007-0525-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-007-0525-5

Search

Navigation