Invariant surfaces in the homogeneous space Sol with constant curvature |
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Authors: | Marian Ioan Munteanu |
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Institution: | University “Al. I. Cuza” of Ia?i, Faculty of Mathematics, , 700506 Ia?i, Romania |
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Abstract: | A surface in homogeneous space is said to be an invariant surface if it is invariant under some of the two 1‐parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curvature. Also, we characterize invariant surfaces that satisfy a linear Weingarten relation. |
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Keywords: | Homogeneous space invariant surface mean curvature Gaussian curvature 53A10 |
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