کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8255589 | 1533710 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Left-invariant Einstein metrics on S3ÃS3
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
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چکیده انگلیسی
The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics g on G=SU(2)ÃSU(2)=S3ÃS3. Einstein metrics are critical points of the total scalar curvature functional for fixed volume. The scalar curvature S of a left-invariant metric g is constant and can be expressed as a rational function in the parameters determining the metric. The critical points of S, subject to the volume constraint, are given by the zero locus of a system of polynomials in the parameters. In general, however, the determination of the zero locus is apparently out of reach. Instead, we consider the case where the isotropy group K of g in the group of motions is non-trivial. When KâZ2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kähler metric, based on representation-theoretic arguments and computer algebra. For the remaining case Kâ
Z2 we present partial results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 128, June 2018, Pages 128-139
Journal: Journal of Geometry and Physics - Volume 128, June 2018, Pages 128-139
نویسندگان
Florin Belgun, Vicente Cortés, Alexander S. Haupt, David Lindemann,