Smooth deformation of holomorphic sections of a Riemannian almost Hermitian fiber bundle through harmonic sections. (English) Zbl 1538.53043
Summary: In this paper we give in the context of sections of a (Riemannian) almost Hermitian fiber bundle a reformulation of a theory of deformation linked to harmonic maps between almost Hermitian manifolds developped by A. Lichnerowicz [in: Sympos. Math., Roma 3, Probl. Evolut. Sist. solare, Nov. 1968 e Geometria, Febb. 1969, 341–402 (1970; Zbl 0193.50101)].
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 55R10 | Fiber bundles in algebraic topology |
Keywords:
almost Hermitian fiber bundle; vertical tension field; holomorphic sections; harmonic sectionsCitations:
Zbl 0193.50101References:
| [1] | Gray, A., Minimal varieties and almost Hermitian submanifolds, Michigan Math. J., 12, 273-287 (1965) · Zbl 0132.16702 · doi:10.1307/mmj/1028999364 |
| [2] | Lichnerowicz, A., Applications harmoniques et varietes \(K\ddot{a}\) hleriennes Proc, 341-402 (1970), Bologna: Symp. Math. III, Bologna · Zbl 0193.50101 |
| [3] | Watson, B., Almost Hermitian submersion, J. Differ. Geom. I, I, 147-165 (1976) · Zbl 0355.53037 |
| [4] | Watson, B., Superminimal fibres in almost Hermitian submersion, Bollettino Unione Mathematica Italiana, 3, 159-172 (2000) · Zbl 0956.53018 |
| [5] | Wood, CM, The gauss section of a Riemannian immersion, J. London Math. Soc., 33, 2, 157-168 (1986) · Zbl 0607.53036 · doi:10.1112/jlms/s2-33.1.157 |
| [6] | Wood, CM, Harmonic almost-complex structures, Compositio Math., 9, 183-212 (1995) · Zbl 0834.53030 |
| [7] | Chinea, D., Harmonicity of holomorphic maps between almost Hermitian manifolds, Canad Math. Bull., 52, 1, 18-27 (2009) · Zbl 1176.53063 · doi:10.4153/CMB-2009-003-4 |
| [8] | Kourouma M.: Harmonische Schnitte Riemanncher Faser bundles. Doctor Thesis at the Ruhr Uni Bochum, Germany (1994) |
| [9] | Kourouma, M., The heat flow for sections of a Riemannian fiber bundle, Africa Math., 11, 29-42 (2000) · Zbl 0989.58011 |
| [10] | Kourouma, M., Harmonic sections of a Riemannian fiber bundle, Africa Math., 8, 18-37 (1997) · Zbl 0910.58008 |
| [11] | Oneill, B., The fondamental equations of a submersion, Michigan Math. J., 13, 459-469 (1966) · Zbl 0145.18602 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
