Osaka Journal of Mathematics

The normal holonomy of $CR$-submanifolds

Antonio J. Di Scala and Francisco Vittone

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Abstract

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a $CR$-submanifold of a complex space form. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation of a Riemannian symmetric space. In case of a totally real submanifold we give two results about reduction of codimension. We describe explicitly the action of the normal holonomy in the case in which the totally real submanifold is contained in a totally real totally geodesic submanifold. In such a case we prove the compactness of the normal holonomy group.

Article information

Source
Osaka J. Math., Volume 54, Number 1 (2017), 17-35.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1488531782

Mathematical Reviews number (MathSciNet)
MR3619746

Zentralblatt MATH identifier
1371.53016

Subjects
Primary: 53B15: Other connections
Secondary: 53B20: Local Riemannian geometry 53B25: Local submanifolds [See also 53C40]

Citation

Di Scala, Antonio J.; Vittone, Francisco. The normal holonomy of $CR$-submanifolds. Osaka J. Math. 54 (2017), no. 1, 17--35. https://projecteuclid.org/euclid.ojm/1488531782


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