Curvature conditions for complex-valued harmonic morphisms

Jonas Nordström

doi:10.1016/j.difgeo.2015.07.004

Curvature conditions for complex-valued harmonic morphisms

Jonas Nordström

Research output: Contribution to journal › Article › peer-review

Abstract

We study the curvature of manifolds which admit a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form.

We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.

Original language	English
Pages (from-to)	44-53
Journal	Differential Geometry and its Applications
Volume	42
DOIs	https://doi.org/10.1016/j.difgeo.2015.07.004
Publication status	Published - 2015

Subject classification (UKÄ)

Geometry

Free keywords

Harmonic morphism
Totally geodesic
Holomorphic

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10.1016/j.difgeo.2015.07.004

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title = "Curvature conditions for complex-valued harmonic morphisms",

abstract = "We study the curvature of manifolds which admit a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.",

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AU - Nordström, Jonas

PY - 2015

Y1 - 2015

N2 - We study the curvature of manifolds which admit a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.

AB - We study the curvature of manifolds which admit a complex-valued submersive harmonic morphism with either, totally geodesic fibers or that is holomorphic with respect to a complex structure which is compatible with the second fundamental form. We also give a necessary curvature condition for the existence of complex-valued harmonic morphisms with totally geodesic fibers on Einstein manifolds.

KW - Harmonic morphism

KW - Totally geodesic

KW - Holomorphic

UR - https://www.scopus.com/pages/publications/84938096492

U2 - 10.1016/j.difgeo.2015.07.004

DO - 10.1016/j.difgeo.2015.07.004

M3 - Article

SN - 1872-6984

VL - 42

SP - 44

EP - 53

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

ER -

Curvature conditions for complex-valued harmonic morphisms

Abstract

Subject classification (UKÄ)

Free keywords

Access to Document

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