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Invariant surfaces in the homogeneous space Sol with constant curvature
Author(s) -
López Rafael,
Munteanu Marian Ioan
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201010083
Subject(s) - mathematics , invariant (physics) , gaussian curvature , geodesic , mathematical analysis , homogeneous , curvature , mean curvature , constant curvature , constant (computer programming) , geometry , combinatorics , mathematical physics , computer science , programming language
A surface in homogeneous space S o l 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.