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Axioms 2018, 7(4), 88; https://doi.org/10.3390/axioms7040088

Exponentially Harmonic Maps into Spheres

1
Dipartimento di Matematica, Informatica, ed Economia, Università degli Studi della Basilicata, Via dell’Ateneo Lucano 10, 85100 Potenza, Italy
2
Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento, 73100 Lecce, Italy
*
Author to whom correspondence should be addressed.
Received: 29 October 2018 / Revised: 16 November 2018 / Accepted: 18 November 2018 / Published: 22 November 2018
(This article belongs to the Special Issue Applications of Differential Geometry)
Full-Text   |   PDF [311 KB, uploaded 22 November 2018]

Abstract

We study smooth exponentially harmonic maps from a compact, connected, orientable Riemannian manifold M into a sphere S m R m + 1 . Given a codimension two totally geodesic submanifold Σ S m , we show that every nonconstant exponentially harmonic map ϕ : M S m either meets or links Σ . If H 1 ( M , Z ) = 0 then ϕ ( M ) Σ . View Full-Text
Keywords: exponentially harmonic map; totally geodesic submanifold; Euler-Lagrange equations exponentially harmonic map; totally geodesic submanifold; Euler-Lagrange equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Dragomir, S.; Esposito, F. Exponentially Harmonic Maps into Spheres. Axioms 2018, 7, 88.

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