Kodai Mathematical Journal

Global lightlike manifolds and harmonicity

C. L. Bejan and K. L. Duggal

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A new class of semi-Riemannian and lightlike manifolds (including globally null) is constructed by using a hypersurface of an orientable Riemannian manifold, endowed with the second fundamental form instead of a metric induced from the ambient space. We show the existence (or non-existence) of harmonic tensor fields and harmonic maps and extend to the semi-Riemannian and lightlike case a result of Chen-Nagano [4]. Then we deal with general lightlike submanifolds immersed in a semi-Riemannian manifold and propose a definition of minimal lightlike submanifolds, which generalize the one given in [7] in the Minkowski space ${\bf R}^4_1$. Several examples are given throughout.

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Kodai Math. J. Volume 28, Number 1 (2005), 131-145.

First available in Project Euclid: 23 March 2005

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Bejan, C. L.; Duggal, K. L. Global lightlike manifolds and harmonicity. Kodai Math. J. 28 (2005), no. 1, 131--145. doi:10.2996/kmj/1111588042. https://projecteuclid.org/euclid.kmj/1111588042.

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