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Totally geodesic horizontally conformal maps
Mustafa, M.T.
1998
Abstract
We obtain a characterization of totally geodesic horizontally conformal
maps by a method which arises as a consequence of the Bochner technique
for harmonic morphisms. As a geometric consequence we show that the
existence of a non-constant harmonic morphism $\textrm{Ø}$ from a
compact Riemannian manifold M$^{m}$ of non-negative Ricci curvature
to a compact Riemannian manifold of non-positive scalar curvature,
forces M$^{m}$ either to be a global Riemannian product of integral
manifolds of vertical and horizontal distributions or to be covered
by a global Riemannian product.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1998)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
M.T. Mustafa, "Totally geodesic horizontally conformal maps", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1998), pp. 45-55.
Languages
en
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