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Session 12. Geometry and Topology of Manifolds
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Conformal submersions with totally umbilical fibers |
Tomasz Zawadzki, University of Łódź, Poland
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Conformal submersions with totally umbilical fibers are a natural
generalisation of Riemannian submersions with totally geodesic
fibers [1]. We show how relations between curvatures of
the domain and the image of a conformal submersion with totally
umbilical fibers yield some obstructions to existence of such
mappings [2]. Also, examples of conformal submersions with
totally umbilical fibers will be presented and a correspondence
between them and Riemannian submersions with totally geodesic fibers will be discussed.
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References- R. H. Escobales Jr, Riemannian submersions
with totally geodesic fibers , Journal of Differential Geometry,
Vol. 10.2, 1975, 253--276.
- T. Zawadzki, Existence conditions for
conformal submersions with totally umbilical fibers ,
Differential Geometry and its Applications, 2014,
http://dx.doi.org/10.1016/j.difgeo.2014.01.010.
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