Students' Seminar
Speaker: Surjeet Singh, IIT Bombay
Host: Suman Kumar Sahoo
Title: Curvature of Curves and Surfaces
Time, day and date: 3:30:00 PM – 4:30:00 PM, Friday, October 23
Venue: Ramanujan Hall (https://meet.google.com/meet/dvs-xapw-vbk)
Abstract: Curvature is a fundamental concept in differential geometry that describes how a curve bends and how a surface behaves locally. The aim of this seminar is to introduce the notion of curvature, beginning with curves and then extending the discussion to surfaces in Euclidean space.
We first discuss the curvature of a regular plane curve and interpret it geometrically as a measure of its bending. Using this notion as a starting point, we introduce parametrized surfaces and discuss their tangent spaces and unit normal fields. We then define the normal curvature of a surface in a given tangent direction and introduce Gaussian curvature as an intrinsic measure of the surface's local geometry. Through suitable examples, we illustrate these concepts and examine how curvature distinguishes different types of surfaces.
The seminar aims to develop an intuitive and mathematical understanding of curvature through definitions, geometric interpretations, and examples, highlighting the transition from the curvature of curves to the curvature of surfaces.