B.-Y. Chen's inequalities for submanifolds of Sasakian space forms
Defever, Filip ; Mihai, Ion ; Verstraelen, Leopold
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 521-529 / Harvested from Biblioteca Digitale Italiana di Matematica
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Recentemente, B.-Y. Chen ha introdotto una nuova serie di invarianti δ⁢n1,…,nk 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 δ⁢n1,…,nk per sottovarietà C-totalmente reali e C⁢R di contatto di una forma spaziale di Sasaki M~⁢c.

Publié le : 2001-06-01
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     author = {Filip Defever and Ion Mihai and Leopold Verstraelen},
     title = {B.-Y. Chen's inequalities for submanifolds of Sasakian space forms},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {521-529},
     zbl = {1121.53320},
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Defever, Filip; Mihai, Ion; Verstraelen, Leopold. B.-Y. Chen's inequalities for submanifolds of Sasakian space forms. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 521-529. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_2_521_0/

[1] Blair, D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., vol. 509, Springer, Berlin, 1976. | MR 467588 | Zbl 0319.53026

[2] Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds, Archiv Math., 60 (1993), 568-578. | MR 1216703 | Zbl 0811.53060

[3] Chen, B.-Y., A Riemannian invariant for submanifolds in space forms and its applications, Geometry and Topology of Submanifolds, 6 (1994), 58-81, World Scientific, Singapore. | MR 1315088 | Zbl 0865.53050

[4] Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions, submitted. | Zbl 1026.53009

[5] Chen, B.-Y.-Dillen, F.-Verstraelen, L.-Vrancken, L., Totally real submanifolds of C⁢Pn satisfying a basic equality, Archiv. Math., 63 (1994), 553-564. | MR 1300757 | Zbl 0816.53034

[6] Chen, B.-Y., F. DILLEN, L. VERSTRAELEN AND Vrancken, L., An exotic totally real minimal immersion of S3 in C⁢P3 and its characterization, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 153-165. | MR 1378838 | Zbl 0855.53011

[7] Defever, F.-Mihai, I.-Verstraelen, L., B.-Y. Chen's inequality for C-totally real submanifolds of Sasakian space forms, Boll. Un. Mat. Ital., 11-B (1997), 365-374. | MR 1459285 | Zbl 0884.53042

[8] Yano, K.-Kon, M., Anti-invariant Submanifolds, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 1976. | MR 425849 | Zbl 0349.53055

[9] Yano, K.-Kon, M., CR-Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser, Boston, 1983. | MR 688816 | Zbl 0496.53037

[10] Yano, K.-Kon, M., Structures on Manifolds, Series in Pure Mathematics, vol. 3, World Scientific, Singapore, 1984. | MR 794310 | Zbl 0557.53001