Abstract
We consider holomorphic and antiholomorphic maps of Kähler manifoldsM andN withM compact. In view of bounds on the Ricci curvature ofM and the holomorphic bisectional curvature ofN, the energy density of the map is constrained to satisfy certain inequalities. One inequality implies that the map is constant. Another specifies the image ofM as a totally geodesic real surface of constant Gaussian curvature inN.
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References
Gauchman, H.: Pinching theorems for totally real minimal submanifolds of ℂP n(c),Tôhoku Math. J. 41 (1989), 249–257.
Mok, N. and Zhang, T. Q.: Curvature characterization of compact Hermitian symmetric spaces,J. Differential Geom. 23 (1986), 15–67.
Sealey, H. C. J.: Harmonic maps of small energy,Bull. London Math. Soc. 13 (1981), 405–408.
Sealey, H. C. J.: Some properties of harmonic mappings, Ph.D. Thesis, University of Warwick, 1980.
Yau, S.-T.: A general Schwarz lemma for Kähler manifolds,Amer. J. Math. 100 (1978), 197–203.
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Gauchman, H., Glazebrook, J.F. Holomorphic maps of Kähler manifolds with constrained energy density. Geom Dedicata 52, 221–226 (1994). https://doi.org/10.1007/BF01278474
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DOI: https://doi.org/10.1007/BF01278474