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Frenet formulae for holomorphic curves in the two quadric

Published online by Cambridge University Press:  17 April 2009

Kichoon Yang
Affiliation:
Department of Mathematics, Arkansas State University, State University, Arkansas 72467, U.S.A.
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Abstract

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We give a complete description of holomorphic curves in the complex two quadric via the method of moving frames. For compact curves a Morse theory type integral formula is derived.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Bryant, R. L., “Conformal and minimal immersions of compact surfaces into the 4-sphere”, J. Differential Geom. 17 (1982), 455473.CrossRefGoogle Scholar
[2]Cartan, E., Théorie des Groupes Finis et Continus et la Geométrie Différentielle traitées par la Méthode du Repère Mobile, (Gauthier-Villars, Paris, 1937).Google Scholar
[3]Chern, S. S., “On the minimal immersions of the two sphere in a space of constant curvature”, Problems in Analysis, (Princeton, N. J., 1970) 2740.Google Scholar
[4]Jensen, G. R., Higher Order Contact of Submanifolds of Homogeneous spaces, (Lecture Notes in Math. Vol. 610, Springer, Berlin, 1977).Google Scholar
[5]Jensen, G. R., Rigoli, M. and Yang, K., “Completely isotropic curves in the quadric”, (to appear).Google Scholar