Geodesic
B.-Y. Chen's inequalities for submanifolds of Sasakian space forms
Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 521-529.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Recentemente, B.-Y. Chen ha introdotto una nuova serie di invarianti $\delta( n_{1} , \ldots, n_{k} )$ riemanniani per ogni varietà riemanniana. Ha anche ottenuto disuguaglianze strette per questi invarianti per sottovarietà di forme spaziali reali e complesse in funzione della loro curvatura media. Nel presente lavoro proviamo analoghe stime per gli invarianti $\delta( n_{1} , \ldots, n_{k} )$ per sottovarietà $C$-totalmente reali e $CR$ di contatto di una forma spaziale di Sasaki $\widetilde{M}(c)$. 
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Defever, Filip; Mihai, Ion; Verstraelen, Leopold. B.-Y. Chen's inequalities for submanifolds of Sasakian space forms. Bollettino della Unione matematica italiana, Série 8, 4B (2001) no. 2, pp. 521-529. http://geodesic.mathdoc.fr/item/BUMI_2001_8_4B_2_a12/

[1] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., vol. 509, Springer, Berlin, 1976. | MR | Zbl

[2] B.-Y. Chen, Some pinching and classification theorems for minimal submanifolds, Archiv Math., 60 (1993), 568-578. | MR | Zbl

[3] B.-Y. Chen, A Riemannian invariant for submanifolds in space forms and its applications, Geometry and Topology of Submanifolds, 6 (1994), 58-81, World Scientific, Singapore. | MR | Zbl

[4] B.-Y. Chen, Some new obstructions to minimal and Lagrangian isometric immersions, submitted. | Zbl

[5] B.-Y. Chen-F. Dillen-L. Verstraelen-L. Vrancken, Totally real submanifolds of $\mathbf{C}P^n$ satisfying a basic equality, Archiv. Math., 63 (1994), 553-564. | MR | Zbl

[6] B.-Y. Chen, F. DILLEN, L. VERSTRAELEN AND L. Vrancken, An exotic totally real minimal immersion of $S^3$ in $\mathbf{C}P^3$ and its characterization, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 153-165. | MR | Zbl

[7] F. Defever-I. Mihai-L. Verstraelen, B.-Y. Chen's inequality for $C$-totally real submanifolds of Sasakian space forms, Boll. Un. Mat. Ital., 11-B (1997), 365-374. | MR | Zbl

[8] K. Yano-M. Kon, Anti-invariant Submanifolds, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 1976. | MR | Zbl

[9] K. Yano-M. Kon, CR-Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser, Boston, 1983. | MR | Zbl

[10] K. Yano-M. Kon, Structures on Manifolds, Series in Pure Mathematics, vol. 3, World Scientific, Singapore, 1984. | MR | Zbl