Abstract
SiaM una sottovarietà totalmente ombelicale di una varietà parakähleriana\(\tilde M\). SeM è anche debolmente antiolomorfa, le curvature bisezionali, ordinarie e normale, diM sono legate da una elegante relazione, da cui discendono interessanti conseguenze.
L'ultimo risultato del lavoro si riferisce alle sottovarietà parakäleriane delle varietà a curvatura sezionale costante.
References
Bejancu A.,Geometry of CR-submanifolds, Reidel, Dordrecht, Holland 1986.
Cartan E.,Leçons sur la géométrie des espaces de Riemann, Gauthier Villar, Paris 1951.
Chen B-Y.,Extrinsic spheres in Kähler manifolds, Michigan Math. J.,23, (1976), 327–330.
Chen B-Y.,Geometry of Submanifolds and its Applications, Science Univ. Tokyo 1981.
Ianus S.,Submanifolds of almost hermitian manifolds, Riv. Mat. Univ. Parma,3 (1994), 123–142.
Ianus S., Rizza G. B.,Submanifolds of constant holomorphic deviation, Boll. Un. Mat. Ital.,11, Suppl. (1997).
Kobayashi S., Nomizu K.,Foundations of Differential Geometry, Vol. 1, 2, Interscience, New York 1963, 1969.
Nomizu K.,Generalized central spheres and the notion of spheres in Riemannian geometry, Tôhoku Math. J.,25 (1973), 129–137.
Rizza G. B.,Varietà parakähleriane, Ann. Mat. Pura Appl.,98 (1974). 47–61.
Rizza G. B.,On the bisectional curvature of a Riemannian manifold, Simon Stevin,61 (1987), 147–155.
Rizza G. B.,On a Bianchi-type identity for the almost Hermitian manifolds, Atti Accad. Naz. Lincei Rend.,82 (1988), 51–59.
Rizza G. B.,Some remarks on parakähler manifolds, Proc. second internat. workshop on Differential Geometry and its applications, Constantza sept. 1995, Anal. Stiint. Univ. Ovidius-Constantza,3 (1995), 113–120.
Ryan P. J.,Kähler manifolds as real hypersurfaces, Duke Math. J.,40 (1973), 207–213.
Sawaki S.,On almost hermitian manifolds satisfying a certain condition on the almost complex structure tensor, Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972.
Takahashi T.,A note on Kählerian hypersurfaces of spaces of constant curvature, Kumamoto J. Sci., (Math.)9 (1972), 21–24.
Vanhecke L.,Submanifolds of almost hermitian manifolds and normal connections, Riv. Mat. Univ. Parma,1 (1975), 239–246.
Vanhecke L.,The Bochner curvature tensor on almost Hermitian manifolds, Geom. Dedicata,6 (1977), 389–397.
Yano K., Kon M.,Anti-invariant submanifolds, Dekker, New York 1976.
Author information
Authors and Affiliations
Additional information
Research partially supported by Ministero Ricerca Scientifica e Tecnologica. Part of the results were announced by the second author in [12].
Rights and permissions
About this article
Cite this article
Ianus, S., Rizza, G.B. Some submanifolds of a parakähler manifold. Rend. Circ. Mat. Palermo 47, 71–80 (1998). https://doi.org/10.1007/BF02844722
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02844722