Geodesic
The curvature of $CR$-submanifolds of a complex projective space that have maximal $CR$-dimension
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2003), pp. 15-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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     title = {The curvature of $CR$-submanifolds of a complex projective space that have maximal $CR$-dimension},
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D. Mar'yana; M. Okumura. The curvature of $CR$-submanifolds of a complex projective space that have maximal $CR$-dimension. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2003), pp. 15-23. http://geodesic.mathdoc.fr/item/IVM_2003_11_a1/

[1] Cecil T. E., Ryan P. J., “Focal sets and real hypersurfaces in complex projective space”, Trans. Amer. Math. Soc., 269:2 (1982), 481–499 | DOI | MR | Zbl

[2] Takagi R., “On homogeneous real hypersurfaces in a complex projective space”, Osaka J. Math., 10:3 (1973), 495–506 | MR | Zbl

[3] Kimura M., “Sectional curvatures of holomorphic planes on a real hypersurface in $P^n(C)$”, Math. Ann., 276 (1987), 487–497 | DOI | MR | Zbl

[4] Lawson H. B., “Local rigidity theorem in rank-$1$ symmetric spaces”, J. Different. Geom., 4 (1970), 349–357 | MR | Zbl

[5] Okumura M., “On some real hypersurfaces of a complex projective space”, Trans. Amer. Math. Soc., 212 (1975), 355–364 | DOI | MR | Zbl

[6] Nirenberg R., Wells R. O. Jr., “Approximation theorems on differentiable submanifolds of a complex manifold”, Trans. Amer. Math. Soc., 142 (1965), 15–35 | DOI | MR

[7] Blair D. E., Contact manifolds in Riemannian geometry, Lect. Notes Math., 509, Springer, Berlin, 1976, 146 pp. | MR | Zbl

[8] Berndt J., Uber Untermanningfaltigkeiten von komplexen Raumformen, Doct. Dissert., Univ. zu Köln, 1989

[9] Kimura M., “Real hypersurfaces and complex submanifolds in complex projective space”, Trans. Amer. Math. Soc., 296:1 (1986), 137–149 | DOI | MR | Zbl

[10] Tumanov A. E., “The geometry of $CR$ manifolds”, Several complex variables, III, Encyclopedia of Math. Sci., 9 VI, Springer-Verlag, 1986, 201–221

[11] Bejancu A., “$CR$-submanifolds of a Kaehler manifold, I”, Proc. Amer. Math. Soc., 69:1 (1978), 135–142 | DOI | MR | Zbl

[12] Djorić M., Okumura M., “$CR$ submanifolds of maximal $CR$ dimension in complex manifolds”, PDE's, Submanifolds and Affine Different. Geom., Banach Center Publ., 57, Inst. Math., Polish Acad. Sci., Warszawa, 2002, 89–99 | MR | Zbl

[13] Kobayashi S., Nomizu K., Foundations of differential geometry, II, Intersci., New York, 1969, 470 pp. | MR | Zbl

[14] Djorić M., Okumura M., “$CR$ submanifolds of maximal $CR$ dimension of complex projective space”, Arch. Math., 71 (1998), 148–158 | DOI | MR | Zbl

[15] O'Neill B., “Isotropic and Kähler immersions”, Canad. J. Math., 17 (1965), 907–915 | MR

[16] Okumura M., “Codimension reduction problem for real submanifolds of complex projective space”, Colloq. Math. Soc. János Bolyai, 56, 1989, 574–585