Nagoya Mathematical Journal

A note on triple systems and totally geodesic submanifolds in a homogeneous space

Arthur A. Sagle

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 32 (1968), 5-20.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118797367

Mathematical Reviews number (MathSciNet)
MR0231945

Zentralblatt MATH identifier
0159.51601

Subjects
Primary: 22.70

Citation

Sagle, Arthur A. A note on triple systems and totally geodesic submanifolds in a homogeneous space. Nagoya Math. J. 32 (1968), 5--20. https://projecteuclid.org/euclid.nmj/1118797367


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References

  • [1] S. Helgason Differential Geometry andSymmetric Spaces, Academic Press, 1962.
  • [2] N. Hicks Submanifolds of semi-Riemannian Manifolds, Rend. Cir. Mat.Palermo, Vol. 12 (1964), 1-13.
  • [3] N.Hicks Notes onDifferential Geometry, Van Nostrand,1965.
  • [4] N.Jacobson LieAlgebras, Interscience,1962.
  • [5] W.G.Lister A structure theory of Lie triple systems, Trans. Amer. Math. Soc, Vol.72 (1952), 217-242.
  • [6] K. Nomizu Invariant affine connections on homogeneous spaces, Amer. J. Math.,Vol. 76 (1954), 33-65.
  • [7] A. Sagle On anti-commutative algebras and general Lie triple systems, Pacific J. Math., Vol. 15 (1965), 281-291.
  • [8] A. Sagle On anti-commutative algebras with an invariant form, Canadian Jol. Math., Vol. 16 (1964), 370-378.
  • [9] A. Sagle On simple algebras obtained from general Lie triple systems, to appear Pacific Jol. Math.
  • [10] A. Sagle On anti-commutative algebras and homogeneous spaces, to appear in Jol. Math, and Mechanics.
  • [11] R.D. Schafer Inner derivations of nonassociative algebras, Bull. Amer. Math. Soc, Vol. 55 (1949), 769-776.
  • [12] I. Singer Differential Geometry, M.I.T. notes (1962).
  • [13] K. Yamaguti On algebras of totally geodesic spaces (Lie triple systems), Jol. Hiroshima Univ., Vol. 21 (1957), 107-113. University of Minnesota