One-Dimensional Metric Foliations in Constant Curvature Spaces

Detlef Gromoll and Karsten Grove

A chapter in Differential Geometry and Complex Analysis, 1985, pp 165-168 from Springer

Abstract: Abstract Let $$Q_c^{n + 1}$$ be a connected space of constant curvature c. In this note we will discuss the structure of 1-dimensional bundlelike Riemannian foliations T of Q, which we call metric foliations for short. The leaves of T are locally fibers of Riemannian submersions, and thus everywhere equidistant. Such foliations T will turn out to be either flat or homogeneous. As a global application we obtain that the Hopf fibrations S2m + 1 → ℂ P m are the only metric fibrations of euclidean spheres with fiber dimension 1.

Keywords: Riemannian Submersion; Riemannian Foliation; Connected Space; Euclidean Sphere; Killing Field (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-69828-6_11

Ordering information: This item can be ordered from
http://www.springer.com/9783642698286

DOI: 10.1007/978-3-642-69828-6_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().