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Holomorphic curves in the complex quadric

Published online by Cambridge University Press:  17 April 2009

Gary R. Jensen ,
Marco Rigoli  and
Kichoon Yang
Gary R. Jensen
Affiliation:
Department of Mathematics, Box 1146, Washington University, Saint Louis, Missouri 63130, United States of America
Marco Rigoli
Affiliation:
International Center for Theoretical Physics, Strada Costiera II, Miramare Trieste, Italy
Kichoon Yang
Affiliation:
Department of Mathematics, Arkansas State University, State University, Arkansas 72467, United States of America.
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Abstract

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A local theory of holomorphic curves in the complex hyperquadric is worked out using the method of moving frames. As a consequence a complete global characterization of totally isotropic curves is obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 125 - 148
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Barbosa, K.J., “On minimal immersions of S2 into S2m.” Trans. Amer. Math. Soc. 210 (1975), 75–106.Google Scholar
[2]Bryant, R.L., “Conformal and minimal immersions of compact surfaces into the 4-sphere”, J. Differential Geom. 17 (1982), 455–473.Google Scholar
[3]Calabi, E., “Quelques applications de l'analyse complexe aux surfaces d'aire minime”, Topics in complex manifolds, Univ. of Montreal, Montreal, Canada, 1968, 59–81.Google Scholar
[4]Chern, S.S., “On minimal spheres in the four sphere”, Selected Papers, Springer Verlag, New York, 1978, 421–434.Google Scholar
[5]Chern, S.S. and Wolfson, J., “Harmonic maps of S2 into complex Grassmann manifold”, Proc. Nat. Acad. Sci. U.S.A., 82 (1985), 2217–2219.Google Scholar
[6]Eells, J. and Wood, J., “Harmonic maps from surfaces to complex projective spaces”, Ad. in Math. 49 (1983), 217–263.Google Scholar
[7]Hoffman, D.A. and Osserman, R., “The geometry of the generalized Gauss map”, Mem. Amec. Math. Soc. 28 (no. 236) (1980)Google Scholar
[8]Jensen, G.R., “Higher order contact of submanifolds of homogeneous spaces”, Lecture Notes in Math. vol. 610, Springer, Berlin, 1977.Google Scholar
[9]Jensen, G.R. and Rigoli, M., “Minimal surfaces in spheres”, Special Volume, Rend. Sem. Math. Fis., Torino, (1983), 75–98.Google Scholar
[10]Jensen, G.R. and Rigoli, M., “A class of harmonic maps from surfaces into real Grassmanians”, Special Volume, Rend. Sem. Mat. Fis., Torino, (1983), 99–116.Google Scholar
[11]Jensen, G.R. and Rigoli, M., ”Quantization of curvature of harmonic two spheres in complex projective space” (preprint).Google Scholar
[12]Kobayashi, S., Transformation Groups in Differential Geometry, Springer-Verlay, New York, 1972.Google Scholar
[13]Lawson, H.B., Lectures on Minimal Submanifolds, Vol. 1, Publish or Perish, Berkeley, 1980.Google Scholar
[14]Ramanathan, J., “Harmonic maps from S2 to G (2, 4)”, J. Differential Geom. 19 (1984), 207–219.Google Scholar
[15]Yang, K., “Frenet formulae for holomorphic curves in the two quadric”, Bull.Austral.Math.Soc. 33 (1986), 195–206.Google Scholar