On the geometry of paracomplex submanifolds

• Autorzy: Al-Ageel A. , Bejancu A.
• Języki publikacji: EN

Abstrakty

EN

We investigate the geometry of both degenerate and non-degenerate para-complex submanifolds of a parahermitian manifold. We stress on basic properties of these submanifolds which are specific to paracomplex geometry. As an example we prove that any degenerate surface of a 4-dimensional parahermitian manifold is totally geodesic.

Słowa kluczowe

EN

paracomplex submanifolds; parakaehlerian manifolds

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 919--932
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Al-Ageel A.

• Department of Mathematics and Computer Science Kuwait University P.O. Box 5969, Safat 13060, Kuwait

autor

Bejancu A.

• Department of Mathematics and Computer Science Kuwait University P.O. Box 5969, Safat 13060, Kuwait

Bibliografia

• [1] C. L. Bejan, 2-codimensional lightlike submanifolds of almost para-Hemitian manifolds, Diff. Geometry and Appl., Brno, 1995; Masaryk Univ., Brno, (1996), 7-17.
• [2] A. Bejancu, The transversal vector bundle of a lightlike submanifold, Bui. Inst. Politehnic Iasi, F.1-4, Séria I, (1994), 9-21.
• [3] A. Bejancu and K. L. Duggal, Lightlike Submanifolds of Semi-Riemannian manifolds and Applications, Kluwer Acad. Publish., Dordrecht, 1996.
• [4] A. Bejancu and F. Etayo, Degenerate hypersurfaces of almost para-Hermitian manifolds, J. Tensor Soc. India, 12, (1994), 39-56.
• [5] V. Cruceanu, P. Fortuny and P. M. Gadea, A survey on paracomplex geometry, Rocky Mountain J. Math., 26, (1996), 83-115.
• [6] M. Dajczer, M. Antonucci, G. Oliveira, P. Lima-Filho and R. Tojeiro, Submanifolds and isometric immersions, Publish or Perish, Inc, Houston, Texas, 1990.
• [7] F. Etayo and M. Fioravanti, CR-Submanifolds of the paracomplex projective space, Publ. Math. Debrecen, 47, (1995), 151-160.
• [8] P. M. Gadea and J. M. Masqué, Classification of homogeneous parakaehlerian space forms, Nova J. Algebra Geom., Vol 1, No2, (1992), 111-124.
• [9] P. M. Gadea and A. A. Montesinos, Spaces of constant paraholomorphic sectional curvature, Pacific J. Math., 136, (1989), 85-101.
• [10] P. M. Gadea and A. A. Montesinos, Totally umbilical pseudo-Riemannian submanifolds of the paracomplex projective space, Czechoslovak Math. J., 44, (1994), 741-756.
• [11] B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
• [12] Z. Olszak, Four-Dimensional para-Hermitian manifolds, Tensor, N.S., 56, (1995), 215-226.
• [13] R. Rosca, CR-Hypersurfaces o champ normal covariant decomposable incluses dans une variété pseudo-riemanniene neutre, C.R. Acad. Sci. Paris, 292, (1981), 287-290.
• [14] R. Rosea, Codimension 2, CR-submanifolds with null covariant decomposable vertical distribution of a neutral manifold, Rend. Mat., (7), 2, (1983), 787-797.
• [15] R. Rosca, CR-sous-variétés co-isotropes d'une variété parakaehlerienne, C.R. Acad. Sci. Paris, 298, (1984), 149-151.