Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 54, Number 1 (2017), 17-35.
The normal holonomy of $CR$-submanifolds
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.
Osaka J. Math., Volume 54, Number 1 (2017), 17-35.
First available in Project Euclid: 3 March 2017
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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