On the geometrical properties of hypercomplex four-dimensional Lie groups
2020 ◽
Vol 27
(1)
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pp. 111-120
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AbstractIn 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 left-invariant vector field X on these spaces and determine all critical points for their energy functional restricted to vector fields of the same length. Furthermore, we give a complete and explicit description of all totally geodesic hypersurfaces of these spaces. The existence of Einstein hypercomplex four-dimensional Lie groups and the non-existence of non-trivial left-invariant Ricci and Yamabe solitons on these spaces are also proved.
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1986 ◽
Vol 6
(5)
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pp. 329-335
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1986 ◽
Vol 7
(3)
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pp. 213-216
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1996 ◽
Vol 11
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pp. 1077-1100
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2020 ◽
Vol 17
(08)
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pp. 2050112
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Vol 62
(5)
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pp. 1116-1130
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1982 ◽
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(2)
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pp. 525-525
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2011 ◽
Vol 61
(2)
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pp. 498-515
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