# On Singular Square Metrics with Vanishing Douglas Curvature

On Singular Square Metrics with Vanishing Douglas Curvature Square metrics $$F=\frac{(\alpha +\beta )^2}{\alpha }$$ F = ( α + β ) 2 α are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $$F=\frac{(b\alpha +\beta )^2}{\alpha }$$ F = ( b α + β ) 2 α . A characterization for such metrics to be of vanishing Douglas curvature is provided. Moreover, many analytical examples are achieved by using a special kinds of metrical deformations called $$\beta$$ β -deformations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

# On Singular Square Metrics with Vanishing Douglas Curvature

, Volume 72 (2) – Jun 22, 2017
16 pages

/lp/springer_journal/on-singular-square-metrics-with-vanishing-douglas-curvature-aNe6KVul7h
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-017-0709-1
Publisher site
See Article on Publisher Site

### Abstract

Square metrics $$F=\frac{(\alpha +\beta )^2}{\alpha }$$ F = ( α + β ) 2 α are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $$F=\frac{(b\alpha +\beta )^2}{\alpha }$$ F = ( b α + β ) 2 α . A characterization for such metrics to be of vanishing Douglas curvature is provided. Moreover, many analytical examples are achieved by using a special kinds of metrical deformations called $$\beta$$ β -deformations.

### Journal

Results in MathematicsSpringer Journals

Published: Jun 22, 2017

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