مترهای فینسلری λ–هم ارز تصویری و پایاهای تصویری فینسلری

نویسندگان
اکبر طیبی
مراد بهادری
حسن صادقی
دانشگاه قم، دانشکدۀ علوم، گروه ریاضی
10.52547/mmr.6.4.621
چکیده
در این مقاله با استفاده از مفهوم مترهای متقارن کروی، مترهای λ –هم‌ارز تصویری را به‌عنوان تعمیمی طبیعی از مترهای هم‌ارز تصویری تعریف می‌کنیم. سپس، مثال‌های غیربدیهی از مترهای λ-هم‌ارز تصویری ارایه می‌کنیم. فرض کنید F و ̅F دو متریک λ-هم‌ارز تصویری روی منیفلد M باشند. ابتدا رابطۀ بین ژئودزی‌های F و ̅F را به‌دست می‌آوریم. سپس ثابت می‌کنیم که هر ژئودزی ازF مضربی از یک ژئودزی ̅F می‌شود و برعکس. در انتها ثابت می‌کنیم که مترهای داگلاس، مترهای ویل و مترهای داگلاس- ویل تعمیم یافته همگی پایاهای λ-هم‌ارز تصویری هستند.
کلیدواژه‌ها
پایای تصویری
متر مسطح تصویری
مترهای هم‌ارز تصویری
متر داگلاس
متر ویل
متر داگلاس- ویل تعمیم یافته

عنوان مقاله English

λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants

نویسندگان English

Akbar Tayebi
Morad Bahadori
Hassan Sadeghi
University of Qom
چکیده English

Introduction

In this paper, by using the concept of spherically symmetric Finsler metric, we define the notion of -projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of -projectively related metrics. Let F and be two -projectively related metrics on a manifold M. We find the relation between the geodesics of F and and prove that any geodesic of F is a multiple of a geodesic of and the other way around. There are several projective invariants of Finsler metrics, namely, Douglas metrics, Weyl metrics and generalized Douglas-Weyl curvature. We prove that the Douglas metrics, Weyl metrics and generalized Douglas-Weyl metrics are -projective invariants.

Material and methods

First we obtain the spray coefficients of a spherically symmetric Finsler metric. By considering it, we define -projectively related metrics which is a generalization of projectively related Finsler metrics. Then we find the geodesics of two -projectively related metrics. We obtain the relation between Douglas, Weyl and generalized Douglas-Weyl curvatures of two -projectively related metrics.

Results and discussion

We find the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature of two -projectively related Finsler metrics. These calculations tell us that these class of Finsler metrics are -projective invariants.

Conclusion

The following conclusions were drawn from this research.

We prove that the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature are -projective invariants.
Let F and be two -projectively related metrics on a manifold M. We show that F is a Berwald metric if and only if is a Berwald metric. ./files/site1/files/64/12.pdf

کلیدواژه‌ها English

Projective invariant
Projectively flat metric
Projectively related metrics
Douglas metric
Weyl metric
Generalized Douglas-Weyl metric
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