Superminimal fibres in an almost Hermitian submersion
Watson, Bill
Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000), p. 159-172 / Harvested from Biblioteca Digitale Italiana di Matematica

Se la varietà base, N, di una submersione quasi-Hermitiana, f:MN, è una G1-varietà e le fibre sono subvarietà superminimali, allora lo spazio totale, M, è G1. Se la varietà base, N, è Hermitiana e le fibre sono subvarietà bidimensionali e superminimali, allora lo spazio totale, M, è Hermitiano.

Publié le : 2000-02-01
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     author = {Bill Watson},
     title = {Superminimal fibres in an almost Hermitian submersion},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3-A},
     year = {2000},
     pages = {159-172},
     zbl = {0956.53018},
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Watson, Bill. Superminimal fibres in an almost Hermitian submersion. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 159-172. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_1_159_0/

[Bo] Borüvka, Sur une classe de surfaces minima plone'es dans un space á quatre dimensions a courbure constante, C. R. Acad. Sci., 187 (1928), 334-336. | JFM 54.0795.02

[Br] Bryant, R., Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Differential Geom., 17 (1982), 455-473. | MR 679067 | Zbl 0498.53046

[Ca] Calabi, E., Minimal immersions of surfaces into Euclidean spheres, J. Differential Geom., 1 (1967), 111-125. | MR 233294 | Zbl 0171.20504

[Fa-Pa] Falcitelli, M.-Pastore, A. M., A note on almost Kähler and nearly Kähler submersions, (preprint), 1998. | Zbl 0967.53023

[Fr1] Friedrich, T., On surfaces in four-spaces, Ann. Global Anal. & Geom., 2 (1984), 257-287. | Zbl 0562.53039

[Fr2] Friedrich, T., On superminimal surfaces, Arch. Math. (Brno), 33 (1997), 41-56. | MR 1464300 | Zbl 1022.53050

[Gr1] Gray, A., Minimal varieties and almost Hermitian submanifolds, Michigan Math. J., 12 (1965), 273-287. | MR 184185 | Zbl 0132.16702

[Gr2] Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-738. | MR 205184 | Zbl 0147.21201

[Gr-He] Gray, A.-Hervella, L., The sixteen classes of almost Hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl.CXXIII (1980), 35-58. | MR 581924 | Zbl 0444.53032

[Gu-Wo] Gudmundsson, S.-Wood, J. C., Harmonic morphisms between almost Hermitian manifolds, Boll. Un. Mat. Ital.11-B, Supp. 2 (1997), 185-197. | MR 1456260 | Zbl 0879.53023

[He-Vid] Hervella, L.-Vidal, E., Nouvelles géométries pseudo-Kähleriennes G1 et G2, C. R. Acad. Sci. Paris283 (1976), 115-118. | MR 431008 | Zbl 0331.53026

[Jo] Johnson, D. L., Kähler submersions and holomorphic connections, J. Diff. Geometry15 (1980), 71-79. | MR 602440 | Zbl 0442.53030

[Ko-No] Kobayashi-Nomizu, K., Foundations of Differential Geometry, Vol. II, Interscience, New York1969. | MR 238225 | Zbl 0175.48504

[Kw] Kwietniewski, St., Über Flachen des vierdimensionalen Raumes, deren sämtliche Tangentialbenen untereinander gleichwinklig sind, und ihre Beziehung zu ebenen Kurven, Dissertation, Zürich, 1902. | JFM 34.0702.01

[Mi-Mo] Micallef, M. J.-Moore, J. D., Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. Math., 127 (1988), 199-227. | MR 924677 | Zbl 0661.53027

[O'N] O'Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459-469. | MR 200865 | Zbl 0145.18602

[Wa1] Watson, B., Almost Hermitian submersions, J. Diff. Geometry, 11 (1976), 147-165. | MR 407784 | Zbl 0355.53037

[Wa2] Watson, B., The four-dimensional Goldberg Conjecture is true for almost Kähler submersions (to appear) J. of Geometry, 1999. | MR 1800470 | Zbl 0979.53081

[Wa-Va1] Watson, B.-Vanhecke, L., J-symmetries and J-linearities of the configuration tensors of an almost Hermitian submersion, Simon Stevin, 51 (1977), 139-156. | MR 482558 | Zbl 0379.53038

[Wa-Va2] Watson, B.-Vanhecke, L., The structure equation of an almost semi-Kähler submersion, Houston Math. J., 5 (1979), 295-305. | MR 546764 | Zbl 0423.53028