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Forum Mathematicum

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Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 30, Issue 3

Issues

Harmonicity and minimality of complex and quaternionic radial foliations

José Carmelo González-Dávila
  • Corresponding author
  • Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna Facultad de Matematicas, 38200 La Laguna, Tenerife, Spain
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Published Online: 2017-10-13 | DOI: https://doi.org/10.1515/forum-2017-0076

Abstract

We construct special classes of totally geodesic almost regular foliations, namely, complex radial foliations in Hermitian manifolds and quaternionic radial foliations in quaternionic Kähler manifolds, and we give criteria for their harmonicity and minimality. Then examples of these foliations on complex and quaternionic space forms, which are harmonic and minimal, are presented.

Keywords: Almost regular distribution; harmonic and minimal distributions; complex and quaternionic projective spaces; complex and quaternionic radial foliations

MSC 2010: 53C20; 53C12; 53C26; 53C55; 53C43

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About the article


Received: 2017-04-07

Revised: 2017-09-15

Published Online: 2017-10-13

Published in Print: 2018-05-01


Supported by D.G.I. (Spain) Project MTM2016-77093-P.


Citation Information: Forum Mathematicum, Volume 30, Issue 3, Pages 785–798, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0076.

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