對(duì)偶平坦Kropina度量（英文）
發(fā)布時(shí)間：2019-01-21 13:25
【摘要】：本文研究了一類具有奇性的芬斯勒度量——廣義Kropina度量.文中給出了刻畫廣義Kropina度量的等價(jià)方程.進(jìn)一步的研究工作表明,由共形1-形式β構(gòu)造的Kropina度量是對(duì)偶平坦的,當(dāng)且僅當(dāng)其中的黎曼度量α是歐氏的,且該1-形式β是常向量場(chǎng).還給出了一類很有意思的非平凡局部對(duì)偶平坦Kropina度量的例子.
[Abstract]:In this paper, we study a class of Fensler metric with singularity, generalized Kropina metric. In this paper, an equivalent equation characterizing the generalized Kropina metric is given. Further studies show that the Kropina metric constructed from conformal 1-form 尾 is dual flat if and only if the Riemannian metric 偽 is Euclidean and the 1-form 尾 is a constant vector field. An interesting class of nontrivial locally dual flat Kropina metrics is also given.
【作者單位】： 東南大學(xué)數(shù)學(xué)學(xué)院;后勤工程學(xué)院基礎(chǔ)部;
【基金】：supported by NSFC(No.11371386) Frontier and Basic Research of Chongqing(No.cstc2014jcyjA00002) the Fundamental Research Funds for Central Universities(No.3207014403,No.3207014203)
【分類號(hào)】：O186.12
本文編號(hào)：2412704
[Abstract]:In this paper, we study a class of Fensler metric with singularity, generalized Kropina metric. In this paper, an equivalent equation characterizing the generalized Kropina metric is given. Further studies show that the Kropina metric constructed from conformal 1-form 尾 is dual flat if and only if the Riemannian metric 偽 is Euclidean and the 1-form 尾 is a constant vector field. An interesting class of nontrivial locally dual flat Kropina metrics is also given.
【作者單位】： 東南大學(xué)數(shù)學(xué)學(xué)院;后勤工程學(xué)院基礎(chǔ)部;
【基金】：supported by NSFC(No.11371386) Frontier and Basic Research of Chongqing(No.cstc2014jcyjA00002) the Fundamental Research Funds for Central Universities(No.3207014403,No.3207014203)
【分類號(hào)】：O186.12
【相似文獻(xiàn)】
相關(guān)期刊論文 前1條
1 黎芳,王佳;Kropina度量的一些射影性質(zhì)及曲率性質(zhì)[J];西南師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2004年03期
，本文編號(hào)：2412704
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