Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (3): 873-889.doi: 10.1016/S0252-9602(10)60085-9

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NATURAL FROBENIUS SUBMANIFOLDS

 LIN Jie-Zhu   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2007-10-20 Revised:2008-04-16 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work is partially supported by NSFC (10631050), NKBRPC (2006CB805905), and China-France-Russian mathematics collaboration grant (34000-3275100) from Sun Yat-Sen University

Abstract:

I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This article will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces.

Key words: Frobenius submanifold, Saito structure

CLC Number: 

  • 53D45
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