On stability of minimal submanifolds in compact symmetric spaces
Compositio Mathematica, Tome 64 (1987) no. 2, pp. 157-189.
@article{CM_1987__64_2_157_0,
     author = {Ohnita, Yoshihiro},
     title = {On stability of minimal submanifolds in compact symmetric spaces},
     journal = {Compositio Mathematica},
     pages = {157--189},
     publisher = {Martinus Nijhoff Publishers},
     volume = {64},
     number = {2},
     year = {1987},
     mrnumber = {916480},
     zbl = {0634.53041},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1987__64_2_157_0/}
}
TY  - JOUR
AU  - Ohnita, Yoshihiro
TI  - On stability of minimal submanifolds in compact symmetric spaces
JO  - Compositio Mathematica
PY  - 1987
SP  - 157
EP  - 189
VL  - 64
IS  - 2
PB  - Martinus Nijhoff Publishers
UR  - http://archive.numdam.org/item/CM_1987__64_2_157_0/
LA  - en
ID  - CM_1987__64_2_157_0
ER  - 
%0 Journal Article
%A Ohnita, Yoshihiro
%T On stability of minimal submanifolds in compact symmetric spaces
%J Compositio Mathematica
%D 1987
%P 157-189
%V 64
%N 2
%I Martinus Nijhoff Publishers
%U http://archive.numdam.org/item/CM_1987__64_2_157_0/
%G en
%F CM_1987__64_2_157_0
Ohnita, Yoshihiro. On stability of minimal submanifolds in compact symmetric spaces. Compositio Mathematica, Tome 64 (1987) no. 2, pp. 157-189. http://archive.numdam.org/item/CM_1987__64_2_157_0/

[C-L-N] B-Y. Chen, P-F. Leung and T. Nagano, Totally geodesic submanifolds of symmetric spaces III, preprint.

[Fe] H. Federer, Geometric measure theory, Die Grundlehren der math. Wissenschaften, Band 153, Springer-Verlag, New York (1969). | MR | Zbl

[F-F] H. Federer and W.H. Fleming, Normal and integral currents, Ann. of Math. 72 (1960) 458-520. | MR | Zbl

[F1] W.H. Fleming, Flat chains over a finite coefficient group, Trans. Amer. Math. Soc. 121 (1966) 160-186. | MR | Zbl

[H1] S. Helgason, Totally geodesic spheres in compact symmetric spaces, Math. Ann. 165 (1966) 309-317. | MR | Zbl

[H2] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, New York, San Francisco, London (1978). | MR | Zbl

[H-W] R. Howard and S.W. Wei, On the existence and non-existence of stable submanifolds and currents in positively curved manifolds and the topology of submanifolds in Euclidean spaces, preprint.

[K] Y. Kimura, The nullity of compact Kaehler manifolds in complex projective spaces, J. Math. Soc. Japan 29 (1977) 561-580. | MR | Zbl

[K-N] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, II, Wiley-Interscience, New York, (1963, 1969). | Zbl

[K-O-T] S. Kobayashi, Y. Ohnita and M. Takeuchi, On instability of Yang-Mills connections, Math. Z. 193 (1986) 165-189. | MR | Zbl

[L-S] H.B. Lawson, Jr. and J. Simons, On stable currents and their application to global problems in real and complex geometry, Ann. of Math. 98 (1973) 427-450. | MR | Zbl

[M-P] W.G. Mckay and J. Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lecture Notes in Pure and Applied Mathematics 69, Marcel Dekker, Inc., New York and Baesel (1981). | MR | Zbl

[N] H. Naitoh, Totally real parallel submanifolds in P n(C), Tokyo J. Math. 29 (1981) 291-306. | MR | Zbl

[O1] Y. Ohnita, Stable minimal submanifolds in compact rank one symmetric spaces, Tohoku Math. J. 38 (1986) 199-217. | MR | Zbl

[O2] Y. Ohnita, Stability of harmonic maps and standard minimal immersions, Tohoku Math. J. 36 (1986) 259-267. | MR | Zbl

[O-T] Y. Ohnita and H. Tasaki, Uniqueness of certain 3-dimensional homologically volume minimizing submanifolds in compact simple Lie groups, Tsukuba J. Math. 10 (1986) 11-16. | MR | Zbl

[S-U] J. Sacks and K. Uhlenbech, The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981) 1-24. | MR | Zbl

[S] J. Simons, Minimal varieties in riemannian manifolds, Ann. of Math. 88 (1968) 62-105. | MR | Zbl

[Ta] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. | MR | Zbl

[Te1] M. Takeuchi, On the fundamental group and the group of isometries of a symmetric space, J. Fac. Sci. Univ. Tokyo 10 (1964) 88-123. | MR | Zbl

[Te2] M. Takeuchi, Modern theory of spherical functions (in Japanese), Iwanami, Tokyo, 1975.

[Te3] M. Takeuchi, Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku Math. J. 36 (1984) 293-314. | MR | Zbl

[Ts] H. Tasaki, Certain minimal or homologically volume minimizing submanifolds in compact symmetric spaces, Tsukuba J. Math. 9 (1985) 117-131. | MR | Zbl

[Wa] N.R. Wallach, Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, Inc., New York (1973). | MR | Zbl

[We] S.W. Wei, Classification of stable currents in the product of spheres, preprint.