On local isometric embeddings of three-dimensional Lie groups
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DOI: 10.1007/s10711-019-00472-y
Abstract: Due to Janet–Cartan’s theorem, any analytic Riemannian manifolds can be locally isometrically embedded into a sufficiently high dimensional Euclidean space. However, for an individual Riemannian manifold ( M , g ), it is in general… read more here.
Keywords: isometrically embedded; dimensional lie; locally isometrically; three dimensional ... See more keywords
Projective unitary representations of infinite-dimensional Lie groups
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DOI: 10.1215/21562261-2018-0016
Abstract: For an infinite dimensional Lie group $G$ modelled on a locally convex Lie algebra $\mathfrak{g}$, we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie… read more here.
Keywords: lie; projective unitary; unitary representations; infinite dimensional ... See more keywords
On the geometrical properties of hypercomplex four-dimensional Lie groups
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DOI: 10.1515/gmj-2018-0003
Abstract: Abstract In this paper, we first classify Einstein-like metrics on hypercomplex four-dimensional Lie groups. Then we obtain the exact form of all harmonic maps on these spaces. We also calculate the energy of an arbitrary… read more here.
Keywords: hypercomplex four; four dimensional; dimensional lie; lie groups ... See more keywords
Sweeping Surfaces in theThree-Dimensional Lie Group
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DOI: 10.3390/sym14040698
Abstract: This paper investigated the rotation minimizing frames that are related to the space curves and the sweeping surfaces that are traced by these frames in the three-dimensional Lie group. Then, the sufficient and necessary conditions… read more here.
Keywords: sweeping surfaces; lie group; surface; dimensional lie ... See more keywords
Sweeping Surfaces Due to Conjugate Bishop Frame in 3-Dimensional Lie Group
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DOI: 10.3390/sym15040910
Abstract: In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-dimensional Lie group G3. With the help of this frame, we derive a parametric representation for a… read more here.
Keywords: lie group; bishop frame; dimensional lie;
Einstein–Maxwell Equations on Four-dimensional Lie Algebras
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DOI: 10.4153/s0008439519000249
Abstract: Abstract We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein–Maxwell equations on four-dimensional Lie algebras. read more here.
Keywords: equations four; dimensional lie; four dimensional; einstein maxwell ... See more keywords