Journal of the Mathematical Society of Japan

`Spindles' in symmetric spaces


Full-text: Open access


We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s -orbits of variable radii. If the s -orbit is symmetric such submanifolds are the most important examples of adapted submanifolds, i.e. of submanifolds of symmetric spaces with curvature invariant tangent and normal spaces.

Article information

J. Math. Soc. Japan, Volume 58, Number 4 (2006), 985-994.

First available in Project Euclid: 21 May 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]

extrinsic geometry submanifolds symmetric spaces Lie triples


QUAST, Peter. `Spindles' in symmetric spaces. J. Math. Soc. Japan 58 (2006), no. 4, 985--994. doi:10.2969/jmsj/1179759533.

Export citation


  • J. Berndt, S. Console and C. Olmos, Submanifolds and holonomy, CRC Press, Boca Raton, 2003.
  • B.-Y. Chen and T. Nagano, Totally geodesic submanifolds of symmetric spaces II, Duke Math. J., 45 (1978), 405–425.
  • B.-Y. Chen and T. Nagano, A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Am. Math. Soc., 308 (1988), 273–297.
  • J.-H. Eschenburg, Higher rank curved Lie triples, J. Math. Soc. Japan, 54 (2002), 551–564.
  • D. Ferus, Symmetric submanifolds of euclidean space, Math. Ann., 247 (1980), 81–93.
  • T. Friedrich, Dirac operators in Riemannian geometry, Amer. Math. Soc., Providence, 2000.
  • S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, New York, 1978.
  • S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures I, J. Math. Mech., 13 (1964), 875–907.
  • T. Nagano and M. S. Tanaka, The involutions of compact symmetric spaces, V, Tokyo J. Math., 23 (2000), 403–416.
  • H. Naitoh, Symmetric submanifolds of compact symmetric spaces, Tsukuba J. Math., 10 (1986), 215–242.
  • H. Naitoh, Grassmann geometries on compact symmetric spaces of general type, J. Math. Soc. Japan, 50 (1998), 557–592.
  • M. Wang and W. Ziller, Symmetric spaces and strongly isotropy irreducible spaces, Math. Ann., 296 (1993), 285–326.