On a class of Ricci quadratic Finsler metrics
Özet
In this paper, we study a class of Finsler warped product metrics with quadratic Ricci curvature. This class is characterized by a partial differential equation. In particular, we obtain a special class of Finsler warped product metrics with quadratic Ricci curvature, indeed, the metrics in this class are Einstein but not Ricci flat. We find an equation that characterizes Finsler warped product metrics as a strongly Ricci-quadratic.
Bu çalışmada, kuadratik Ricci eğriliği olan bükülmüş çarpımlı Finsler metriklerinin bir sınıfı incelenmiştir. Bu sınıf, kısmi bir diferansiyel denklem ile karakterize edilmiş olup, kuadratik Ricci eğriliği olan bükülmüş çarpımlı Finsler metriklerinin bir özel sınıfı olan bu metrikler Einstein'dır, ama Ricci düz değiller. Ayrıca kuadratik kuvvetli Ricci eğriliği olan bükülmüş çarpımlı Finsler metriklerini bir sınıfı Finsler'in çarpık ürün metriklerini güçlü bir Ricci-kuadratik olarak nitelendiren bir denklem bulunmuştur.
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