Abstract
This paper is devoted to the study of the global theory of certain mappings between Riemannian manifolds. We generalize results by Vilms, Yano and Ishihara, and study in detail projective, umbilical and harmonic maps.
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Brito, F.;Walczak, P.: Totally geodesic foliations with integrable normal bundles.Bol. Soc. Bras. Mat. 17 (1986), 41–46.
Har'El, Z.: Harmonic mappings and distortion theorems.Tensor, New Ser. 30 (1976), 47–54.
Har'El, Z.: Projective mappings and distortion theorems.J. Differ. Geom. 15 (1980), 97–106.
Ranjan, A.: Structural equations and an integral formula for foliated manifolds.Geom. Dedicata 20 (1986), 85–91.
Sinyukov, N.S.:Geodesic mappings of Riemannian spaces. Nauka, Moscow 1979.
Sulanke, R.;Wintgen, P.:Differentialgeometrie und Faserbündel. Dt. Verlag d. Wiss., Berlin 1972.
Stepanov, S.E.: On the global theory of projective submersions and immersions.Differ. Geom. Mnogoobrazij Figur 22 (1993), 101–104.
Stepanov, S.E.: Bochner's technique in the theory of Riemannian almost product structures.Math. Notes 48 (1990), 778–781.
Stepanov, S.E.:A geometrical obstruction to the existence of totally umbilical distribution on a compact manifold. Webs and quasigroups. Kalinin Gos. Univ., Kalinin 1990, 135–137.
Stepanov, S.E.: A class of Riemannian almost product structures.Izv. Vyssh. Uchebn. Zaved. Mat. 7 (1989), 40–46.
Vilms, J.: Totally geodesic maps.J. Differ. Geom. 4 (1970), 73–79.
Yano, K.;Ishihara, S.: Harmonic and relatively affine mappings.J. Differ. Geom. 10 (1975), 501–509.
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The work of the author was supported by RBRF, grant 94-01-01595 (Russia).
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Stepanov, S.E. On the global theory of some classes of mappings. Ann Glob Anal Geom 13, 239–249 (1995). https://doi.org/10.1007/BF00773658
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DOI: https://doi.org/10.1007/BF00773658