Abstract
In this paper we prove that a (ϕ,J)-holomorphic mapf:M→N (i.e.f *oϕ=Jof *) from a Trans-Sasaki manifold to a nearly Kähler manifold is a harmonic map. We also study the stability of a such map whenM is a compact Trans-Sasaki manifold andN is a Kähler manifold.
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References
Blair D. E.,Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag (1976).
Dragomir S., Wood J.,Sottovarietà minimali ed applicazioni armoniche Bologna (1989).
Eells J., Lemaire L.,Selected topics in harmonic maps, C.B.M.S. Regional Conf. Series50, Amer. Math. Society (1983).
Eells J., Lemaire L.,Another report on harmonic maps, Bulletin London Math. Society20 (1988), 385–524.
Gherghe C.,Harmonic maps on Kenmotsu manifolds (to appear).
Ianus S., Pastore A. M.,Harmonic maps on contact metric manifolds, Annales Math. Blaise Pascal2 (2) (1995), 43–53.
Ianus S., Pastore A. M.,Some foliations defined by f-structures with parallelizable kernel (preprint).
Ianus S., Rizza G.B.,Submanifolds of Constant Holomorphic Deviation, Bulletino UMI Suppl. fasc. 2,11-B, (1997), 115–124.
Janssens D., Vanhecke L.,Almost contact structures and curvature tensor, Kodai Math. J.4 (1981), 1–27.
Kenmotsu K.,A class of almost contact Riemannian manifolds, Tohoku Math. J.24 (1972), 93–103.
Oubina A.,New class of an almost contact metric structure. Publ. Math. Debrecen32 (1985), 187–193.
Papagiuc N.,Semi-invariant submanifolds in Kenmotsu manifolds, Rediconti di Mat.3 (1985), 607–622.
Toth G.,Harmonic and Minimal Maps With Application in Geometry and Physics, Ellis Horwood limited (1984).
Urakawa H.,Calculus of Variation and Harmonic Maps, Translations of Mathematical Monographs, 132. American Math Society, Providence, RI, (1993).
Urakawa H.,Stability of harmonic maps and eingenvalues of Laplacian, Curvature and Topology of Riemannian manifolds L.N.M.1201 Springer-Verlag (1986), 285–307.
Watson,The differential Geometry of two types of almost contact metric submersions, The Math. Heritage of C. F. Gauss 827–861 World Sci. (1991).
Yano K., Kon M.,Structures on manifolds, World Sci. Publ. Singapore, Tome3 (1984).
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Gherghe, C. Harmonic maps on Trans-Sasaki manifolds. Rend. Circ. Mat. Palermo 48, 477–486 (1999). https://doi.org/10.1007/BF02844337
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DOI: https://doi.org/10.1007/BF02844337