An extension of a result of H. Hopf to Kähler submanifolds of ℝ n

Maria J. Ferreira; Marco Rigoli; Renato Tribuzy

Rendiconti del Seminario Matematico della Università di Padova (1995)

  • Volume: 94, page 11-15
  • ISSN: 0041-8994

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Ferreira, Maria J., Rigoli, Marco, and Tribuzy, Renato. "An extension of a result of H. Hopf to Kähler submanifolds of $\mathbb {R}^n$." Rendiconti del Seminario Matematico della Università di Padova 94 (1995): 11-15. <http://eudml.org/doc/108364>.

@article{Ferreira1995,
author = {Ferreira, Maria J., Rigoli, Marco, Tribuzy, Renato},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {immersions of Kähler manifolds in Euclidean spaces; parallel -component of complex bilinear extension of the second fundamental form; product immersions},
language = {eng},
pages = {11-15},
publisher = {Seminario Matematico of the University of Padua},
title = {An extension of a result of H. Hopf to Kähler submanifolds of $\mathbb \{R\}^n$},
url = {http://eudml.org/doc/108364},
volume = {94},
year = {1995},
}

TY - JOUR
AU - Ferreira, Maria J.
AU - Rigoli, Marco
AU - Tribuzy, Renato
TI - An extension of a result of H. Hopf to Kähler submanifolds of $\mathbb {R}^n$
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1995
PB - Seminario Matematico of the University of Padua
VL - 94
SP - 11
EP - 15
LA - eng
KW - immersions of Kähler manifolds in Euclidean spaces; parallel -component of complex bilinear extension of the second fundamental form; product immersions
UR - http://eudml.org/doc/108364
ER -

References

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  1. [C] E. Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Diff. Geom., 1 (1976), pp. 111-125. Zbl0171.20504MR233294
  2. [E] J. Erbacher, Reduction of the codimension of an isometric immersion, J. Diff. Geom., 5 (1971) pp. 333-340. Zbl0221.53031MR288701
  3. [EW] J. Eells - J.C. Wood, Harmonic maps from surfaces to complex projective spaces, Advances in Math., 49 (1983), pp. 217-263. Zbl0528.58007MR716372
  4. [FT] M.J. Ferreira - R. Tribuzy, Kählerian submanifolds of Rn with pluriharmonic Gauss maps, to appear in Bulletin de la Societé Mathématique de Belgique. Zbl0807.53051MR1315847
  5. [H] H. Hopf, Differential Geometry in the Large, LNM, 1000 (Springer, 1983). Zbl0526.53002MR707850
  6. [KW] S. Kobayashi - H.H. Wu, On holomorphic sections of certain Hermitian vector bundles, Math. Ann., 189 (1970), pp. 1-4. Zbl0189.52201MR270392
  7. [M] J.D. Moore, Isometric immersions of Riemannian products, J. Diff. Geom., 5 (1971), pp. 159-168. Zbl0213.23804MR307128
  8. [W] H.C. Wente, Counter example to a conjecture of H. Hopf, Pac. J. Math., 121 (1986), pp. 193-243. Zbl0586.53003MR815044
  9. [Y] S.T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Mauge-Ampere equation, I Comm. Pure Appl. Math., 31 (1978), pp. 339-411. Zbl0369.53059MR480350

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