On Cauchy-Riemann submanifolds whose local geodesic symmetries preserve the fundamental form

• Autorzy: Sorin Dragomir , Mauro Capursi
• Języki publikacji: EN

Abstrakty

EN

We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.

Słowa kluczowe

EN

Cauchy-Riemann submanifolds

Kategorie tematyczne

• 53C55: Hermitian and K\"ahlerian manifolds
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 2
• Strony: 99-103

Daty

wydano

1992

otrzymano

1990-01-15

Twórcy

autor

Sorin Dragomir

• Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651, U.S.A.

autor

Mauro Capursi

• Dipartimento di Matematica, Università Degli Studi di Bari, 70125 Bari, Italy

Bibliografia

• [1] B. Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Agnew. Math. 325 (1981), 28-67.
• [2] S. Dragomir, Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds, I, II, Geom. Dedicata 28 (1988), 181-197; Atti Sem. Mat. Fis. Univ. Modena 37 (1989), 1-11.
• [3] S. Dragomir, On submanifolds of Hopf manifolds, Israel J. Math. (2) 61 (1988), 199-210.
• [4] A. Gray, The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J. 20 (1973), 329-344.
• [5] K. Sekigawa and L. Vanhecke, Symplectic geodesic symmetries on Kaehler manifolds, Quart. J. Math. Oxford Ser. (2) 37 (1986), 95-103.
• [6] I. Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. 12 (1979), 263-284.
• [7] K. Yano, On a structure defined by a tensor field of type (1,1) satisfying f³+f=0, Tensor (N.S.) 14 (1963), 99-109.
• [8] K. Yano and M. Kon, Generic submanifolds, Ann. Mat. Pura Appl. 123 (1980), 59-92.
• [9] K. Yano and M. Kon, Cr Submanifolds of Kaehlerian and Sasakian Manifolds, Progr. Math. 30, Birkhäuser, Boston 1983.