Grassmann geometries on compact symmetric spaces of general type

Hiroo NAITOH

doi:10.2969/jmsj/05030557

Hiroo NAITOH

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JOURNAL FREE ACCESS

1998 Volume 50 Issue 3 Pages 557-592

DOI https://doi.org/10.2969/jmsj/05030557

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Published: 1998 Received: September 06, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. Berger, Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup. 74 (1957), 85-177.
2) N. Bourbaki, Groupes et algèbres de Lie, Hermann, Paris, 1968.
3) H. Freudenthal-H, de Vries, Linear Lie Groups, Academic Press, New York, London, 1969.
4) R. Harvey-H. B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47-157.
5) S. Helgason, Differential Geometry, Lie groups and Symmetric spaces, Academic Press, New York, 1978.
6) J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Splinger-Verlag, New York, 1972.
7) S. Kobayashi-K. Nomizu, Foundations of differential geometry I, II, Wiley, New York, 1963, 1969.
8) J. D. Moore, Isometric immersions of riemannian products, J. Differential Geometry 5 (1971), 159-168.
9) S. Murakami, Sur la classification des algèbres de Lie réelles et simples, Osaka J. Math. 2 (1965), 291-307.
10) H. Naitoh, Symmetric submanifolds of compact symmetric spaces, Tsukuba J. Math. 10 (1986), 215-242.
11) H. Naitoh, Submanifolds of symmetric spaces and Gauss maps, Adv. Stu. in Pure Math. 22 (1993), 197-211.
12) H. Naitoh, Compact simple Lie algebras with two involutions and submanifolds of compact symmetric spaces I, II, Osaka J. Math. 30 (1993), 653-690, 691-732.
13) H. Naitoh, Grassmann geometries on compact symmetric spaces of classical type (to appear).
14) H. Naitoh, Grassmann geometries on compact symmetric spaces of exceptional type (to appear).
15) H. Naitoh-M. Takeuchi, Symmetric submanifolds of symmetric spaces, Sugaku Exp. 2 (1989), 157-188.
16) M. Takeuchi, Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku J. Math. 36 (1984), 293-314.
17) C. Yen, Sur la classification des algèbres de Lie simples réeles et les figures de Schlafli associées, Science Record, New Ser. (China) 3 (1959), 270-275.
18) C. Yen, Sur les espaces symétriques non compacts, Scientia Sinica 14 (1965), 31-38.

Right : [1] M. Berger, Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup. 74 (1957), 85-177.
[2] N. Bourbaki, Groupes et algèbres de Lie, Hermann, Paris, 1968.
[3] H. Freudenthal-H, de Vries, Linear Lie Groups, Academic Press, New York, London, 1969.
[4] R. Harvey-H. B. Lawson, Calibrated geometries, Acta Math. 148 (1982), 47-157.
[5] S. Helgason, Differential Geometry, Lie groups and Symmetric spaces, Academic Press, New York, 1978.
[6] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Splinger-Verlag, New York, 1972.
[7] S. Kobayashi-K. Nomizu, Foundations of differential geometry I, II, Wiley, New York, 1963, 1969.
[8] J. D. Moore, Isometric immersions of riemannian products, J. Differential Geometry 5 (1971), 159-168.
[9] S. Murakami, Sur la classification des algèbres de Lie réelles et simples, Osaka J. Math. 2 (1965), 291-307.
[10] H. Naitoh, Symmetric submanifolds of compact symmetric spaces, Tsukuba J. Math. 10 (1986), 215-242.
[11] H. Naitoh, Submanifolds of symmetric spaces and Gauss maps, Adv. Stu. in Pure Math. 22 (1993), 197-211.
[12] H. Naitoh, Compact simple Lie algebras with two involutions and submanifolds of compact symmetric spaces I, II, Osaka J. Math. 30 (1993), 653-690, 691-732.
[13] H. Naitoh, Grassmann geometries on compact symmetric spaces of classical type (to appear).
[14] H. Naitoh, Grassmann geometries on compact symmetric spaces of exceptional type (to appear).
[15] H. Naitoh-M. Takeuchi, Symmetric submanifolds of symmetric spaces, Sugaku Exp. 2 (1989), 157-188.
[16] M. Takeuchi, Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tohoku J. Math. 36 (1984), 293-314.
[17] C. Yen, Sur la classification des algèbres de Lie simples réeles et les figures de Schlafli associées, Science Record, New Ser. (China) 3 (1959), 270-275.
18) C. Yen, Sur les espaces symétriques non compacts, Scientia Sinica 14 (1965), 31-38.

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