On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds

Bing Wu Ye

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 3, page 273-280
  • ISSN: 0044-8753

Abstract

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Let f : M G ( m , n ) be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by f to have degenerate ' -transform or ' ' -transform are given.

How to cite

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Ye, Bing Wu. "On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds." Archivum Mathematicum 041.3 (2005): 273-280. <http://eudml.org/doc/249495>.

@article{Ye2005,
abstract = {Let $f:M\rightarrow G(m,n)$ be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by $f$ to have degenerate $\partial ^\{\prime \}$-transform or $\partial ^\{\prime \prime \}$-transform are given.},
author = {Ye, Bing Wu},
journal = {Archivum Mathematicum},
keywords = {complex Grassmann manifold; harmonic map; harmonic sequence; genus; the generalized Frenet formulae; harmonic map; harmonic sequence; genus; generalized Frenet formulae},
language = {eng},
number = {3},
pages = {273-280},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds},
url = {http://eudml.org/doc/249495},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Ye, Bing Wu
TI - On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 3
SP - 273
EP - 280
AB - Let $f:M\rightarrow G(m,n)$ be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by $f$ to have degenerate $\partial ^{\prime }$-transform or $\partial ^{\prime \prime }$-transform are given.
LA - eng
KW - complex Grassmann manifold; harmonic map; harmonic sequence; genus; the generalized Frenet formulae; harmonic map; harmonic sequence; genus; generalized Frenet formulae
UR - http://eudml.org/doc/249495
ER -

References

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  1. Chern S. S., Wolfson J. G., Harmonic maps of the two-spheres into a complex Grassmann manifold II, Ann. Math. 125 (1987), 301–335. (1987) MR0881271
  2. Wolfson J. G., Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds, J. Diff. Geom. 27 (1988), 161–178. (1988) MR0918462
  3. Liao R., Cyclic properties of the harmonic sequence of surfaces in CP n , Math. Ann. 296 (1993), 363–384. (1993) MR1219907
  4. Dong Y. X., On the isotropy of harmonic maps from surfaces to complex projective spaces, Inter. J. Math. 3 (1992), 165–177. (1992) Zbl0759.58013MR1146809
  5. Jensen G. R., Rigoli M., On the isotropy of compact minimal surfaces in CP n , Math. Z. 200 (1989), 169–180. (1989) MR0978292
  6. Burstall F. E., Wood J. C., The construction of harmonic maps into complex Grassmannian, J. Diff. Geom. 23 (1986), 255–297. (1986) MR0852157
  7. Uhlenbeck K., Harmonic maps into Lie groups (classical solutions of the chiral model, J. Diff. Geom. 30 (1989), 1–50. (1989) Zbl0677.58020MR1001271
  8. Shen Y. B., Dong Y. X., On pseudo-holomorphic curves in complex Grassmannian, Chin. Ann. Math. 20B (1999), 341–350. (1999) MR1749475
  9. Eschenburg J. H., Guadalupe I. V., Tribuzy R. A., The fundamental equations of minimal surfaces in CP 2 , Math. Ann. 270 (1985), 571–598. (1985) MR0776173
  10. Eells J., Wood J. C., Harmonic maps from surfaces to complex projective spaces, Adv. Math. 49 (1983), 217–263. (1983) Zbl0528.58007MR0716372

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