Prolongations of differential systems and its topology

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740054
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hiroshima University
• Principal Investigator: SHIBUYA Kazuhiro 広島大学, 理学(系)研究科(研究院), 准教授 (00569832)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 微分式系 / 微分方程式の幾何学

Outline of Final Research Achievements

A subbundle of the tangent bundle on a manifold are called a differential system. The theory of differential systems is known as a method to study partial differential equations. Partial differential equations are used to describe natural phenomena, therefore to study partial differential equations is important. Especially, to study partial differential equations having singularities is garnering attention. In this situation, we study partial differential equations having singularities from the view point of the theory of differential systems and get fundamental theorems for the equations. We apply the above result to second and third order partial differential equations with one dependent and two independent variables and obtain the characterization of the existence of solutions.

Free Research Field

微分幾何学