Acta mathematica scientia, Series B >
NATURAL FROBENIUS SUBMANIFOLDS
Received date: 2007-10-20
Revised date: 2008-04-16
Online 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
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
LIN Jie-Zhu . NATURAL FROBENIUS SUBMANIFOLDS[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 873 -889 . DOI: 10.1016/S0252-9602(10)60085-9
[1] Dubrovin B. Geometry of 2D topological field theories//Integrable systems and quantum groups (Montecatini Terme, 1993). Lecture Notes in Math, Vol. 1620. Berlin: Springer, 1996: 120--348
[2] Hertling C. Frobenius manifolds and moduli spaces for singularities//Cambridge Tracts in Mathematics. Vol. 151. Cambridge: Cambridge University Press, 2002
[3] Sabbah C. D\'eformations isomonodromiques et vari\'et\'es de Frobenius. Savoirs Actuels (Les Ulis). [Current Scholarship (Les Ulis)],
EDP Sciences, Les Ulis, 2002, Math\'ematiques (Les Ulis). [Mathematics (Les Ulis)]
[4] Strachan I A B. Frobenius submanifolds. J Geom Phys, 2001, 38(3/4): 285--307
[5] Strachan I A B. Frobenius manifolds: natural submanifolds and induced bi-Hamiltonian structures. Differential Geom Appl, 2004, 20(1): 67--99.
[6] Willmore T J. Riemannian geometry//Oxford Science Publications. New York: The Clarendon Press Oxford University Press, 1993.
[7] Manin Y I. Frobenius manifolds, quantum cohomology, and moduli spaces//American Mathematical Society Colloquium Publications. Vol. 47. American Mathematical Society, Providence, RI, 1999
/
| 〈 |
|
〉 |