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- W2375752422 abstract "In this paper,we obtain a sufficient and necessary condition for a class of(α,β)-metrics in the form of F=αφ(β/α) to be Einstein metrics,where φ(s)=ep(s),and p(s) is a polynomial in s of degree k(k≥1),α is a Riemannian metric,and β is a 1-form.With the correct value of Riemannian curvature and Ricci curvature,the local equivalent equations can be obtained.Through a series of complicated calculations by Maple program,the equations can be analyzed to get the key result of this paper.Here,we mainly use some algebra knowledge with respect to polynomials.Actually,we find that these kinds of metrics are Einsteinnian if and only if they are Ricci-flat." @default.
- W2375752422 created "2016-06-24" @default.
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- W2375752422 date "2011-01-01" @default.
- W2375752422 modified "2023-09-26" @default.
- W2375752422 title "A Class of Einstein(α,β)-Metrics with Exponent Form" @default.
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