Geodesic
PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn
Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 331-339

Voir la notice de l'article provenant de la source Cambridge University Press

Let M be an n-dimensional totally real minimal submanifold in CPn. We prove that if M is semi-parallel and the scalar curvature τ, , then M is an open part of the Clifford torus Tn ⊂ CPn. If M is semi-parallel and the scalar curvature τ, , then M is an open part of the real projective space RPn.
DOI : 10.1017/S001708950900500X
Mots-clés : 53C42, 53C40, 53C20 
MURATHAN, CENGİZHAN; ÖZGÜR, CİHAN. PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn. Glasgow mathematical journal, Tome 51 (2009) no. 2, pp. 331-339. doi: 10.1017/S001708950900500X
@article{10_1017_S001708950900500X,
     author = {MURATHAN, CENG\.IZHAN and \"OZG\"UR, C\.IHAN},
     title = {PINCHING {THEOREMS} {FOR} {TOTALLY} {REAL} {MINIMAL} {SUBMANIFOLDS} {IN} {CPn}},
     journal = {Glasgow mathematical journal},
     pages = {331--339},
     year = {2009},
     volume = {51},
     number = {2},
     doi = {10.1017/S001708950900500X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950900500X/}
}
TY  - JOUR
AU  - MURATHAN, CENGİZHAN
AU  - ÖZGÜR, CİHAN
TI  - PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn
JO  - Glasgow mathematical journal
PY  - 2009
SP  - 331
EP  - 339
VL  - 51
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950900500X/
DO  - 10.1017/S001708950900500X
ID  - 10_1017_S001708950900500X
ER  - 
%0 Journal Article
%A MURATHAN, CENGİZHAN
%A ÖZGÜR, CİHAN
%T PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CPn
%J Glasgow mathematical journal
%D 2009
%P 331-339
%V 51
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950900500X/
%R 10.1017/S001708950900500X
%F 10_1017_S001708950900500X

[1] 1.Amarzaya, A. and Ohnita, Y., Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces, Tohoku Math. J. 55 (4) (2003), 583–610. Google Scholar | DOI

[2] 2.Calabi, E., Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens, Mich. Math. J. 5 (1958), 105–126. Google Scholar | DOI

[3] 3.Chen, B. Y. and Ogiue, K., On totally real submanifolds, Trans. Am. Math. Soc. 193 (1974), 257–266. Google Scholar | DOI

[4] 4.Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom. 25 (1985), 192–200. Google Scholar | DOI

[5] 5.Deprez, J., Semi-parallel hypersurfaces, Rend. Sem. Mat. Univers. Politecn. Torino, 44 (1986), 303–316. Google Scholar

[6] 6.Dillen, F., Semi-parallel hypersurfaces of a real space form, Israel J. Math. 75 (1991), 193–202. Google Scholar | DOI

[7] 7.Ejiri, N., Totally real minimal submanifolds in a complex projective space, Proc. Am. Math. Soc. 86 (1982), no. 3, 496–497. Google Scholar | DOI

[8] 8.Ferus, D., Immersions with parallel second fundamental form, Math. Z. 140 (1974), 87–93. Google Scholar | DOI

[9] 9.Li, A. M. and Zhao, G., Totally real minimal submanifolds in CP n, Arch. Math. (Basel) 62 (1994), 562–568. Google Scholar | DOI

[10] 10.Lumiste, Ü., Semi-symmetric submanifolds as the second order envelope of symmetric submanifolds, Proc. Eston. Acad. Sci. Phys. Math. 39 (1990), 1–8. Google Scholar

[11] 11.Naitoh, H., Totally real parallel submanifolds in P n(C), Tokyo J. Math. 4 (2) (1981), 279–306. Google Scholar | DOI

[12] 12.Perrone, D., n-dimensional totally real minimal submanifolds of CP n, Arch. Math. (Basel) 68 (1997), 347–352. Google Scholar | DOI

[13] 13.Takeuchi, M., Parallel submanifolds of space forms, Manifolds and Lie groups (Notre Dame, IN, 1980), pp. 429–447, Progr. Math., 14 (Birkh äuser, Boston, MA, 1981). Google Scholar | DOI

[14] 14.Yano, K. and Kon, M., Anti-invariant submanifolds, Lecture Notes in Pure and Applied Mathematics, No. 21. (Marcel Dekker, New York and Basel, 1976). Google Scholar

[15] 15.Yano, K. and Kon, M., Structures on manifolds, Series in Pure Mathematics, 3. (World Scientific, Singapore, 1984). Google Scholar

Cité par Sources :