Browsing Doctoral Dissertations by Author "Šukilović, Tijana"
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Šukilović, Tijana (Beograd , 2015)[more][less]
Abstract: In the present work we classify left invariant metrics of arbitrary signature on four-dimensional nilpotent Lie groups. Their geometry is extensively studied with special emphasis on holonomy groups and decomposability of metrics. Also, isometry groups are completely described and we give examples of metrics where strict inequalities Isplit < Iaut < I hold. It is interesting that Walker metrics appear as the underlying structure of neutral signature metrics on the nilpotent Lie groups with degenerate center. We nd necessary and su cient condition for them to locally admit nilpotent group of isometries. Finally, we solve the problem of projectively equivalent metric on four-dimensional nilpotent Lie groups by showing that left invariant metric is either geometrically rigid or have projectively equivalent metrics that are also a nely equivalent. All a nely equivalent metrics are left invariant, while their signature may change. URI: http://hdl.handle.net/123456789/4453 Files in this item: 1
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