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3 results

  • CLASSIFICATION OF LAGRANGIAN WILLMORE SUBMANIFOLDS OF THE NEARLY KAEHLER 6-SPHERE $S^6(1)$ WITH CONSTANT SCALAR CURVATURE

  • HAIZHONG LI, GUOXIN WEI
  • Journal:
    Glasgow Mathematical Journal / Volume 48 / Issue 1 / January 2006
    Published online by Cambridge University Press:
    24 March 2006, pp. 53-64
    Print publication:
    January 2006
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  • In this paper, we classify 3-dimensional Lagrangian Willmore submanifolds of the nearly kaehler 6-sphere $S^6(1)$ with constant scalar curvature.

  • Generalized Minkowski formulae for compact submanifolds of a Riemannian manifold

  • Part of
  • Geoffrey Howard Smith
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 36 / Issue 3 / June 1984
    Published online by Cambridge University Press:
    09 April 2009, pp. 378-388
    Print publication:
    June 1984
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  • In 1903 H. Minkowski obtained two integral formulae for closed convex surfaces in three dimensional Euclidean space. In this paper we obtain generalised Minkowski formulae on compact orientable immersed submanifolds of an arbitrary Riemannian manifold. By successive specialisation we indicate how known integral theorems can be obtained as particular cases of our result.

  • Conformal variation of a hypersurface of constant mean curvature in an einstein space

  • Part of
  • Geoffrey Howard Smith
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 33 / Issue 2 / October 1982
    Published online by Cambridge University Press:
    09 April 2009, pp. 229-234
    Print publication:
    October 1982
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  • Let a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.