## What is a regular surface?

A subset is called a regular surface if for each point , there exists a neighborhood of in and a map of an open set onto such that. 1.

**What is local differential geometry?**

From Encyclopedia of Mathematics. The part of differential geometry that studies properties of geometrical forms, in particular curves and surfaces, “in the small” . In other words, the structure of a geometrical form is studied in a small neighbourhood of an arbitrary point of it.

**WHAT IS curve and surface?**

A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it. Surface is a plane or area of the object. For example, a circle is an example of curved-shape. For example, a cube has all its surfaces or faces of square shape.

### How do you determine if a surface is smooth?

A surface is said to be smooth if it does not have singular points, in other words, if it has a (unique) tangent plane at every point.

**Who is called as father of geometry?**

Euclid, The Father of Geometry.

**Is differential geometry pure math?**

Abstract: Normally, mathematical research has been divided into “pure” and “applied,” and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas.

#### Is there a second edition of docarmo differential geometry?

Docarmo seems to be used in a lot of differential geometry classes, and this second edition cleans up errors in the earlier edition (and adds a few) and expands on some of the material and problems. The book is clearly for classroom use and less for self-study.

**Who was Manfredo do Carmo and what did he do?**

Manfredo do Carmo. Manfredo Perdigão do Carmo (15 August 1928 – 30 April 2018) was a Brazilian mathematician, doyen of Brazilian differential geometry, and former president of the Brazilian Mathematical Society. He was at the time of his death an emeritus researcher at the IMPA.

**How to read differential geometry of curves and surfaces?**

The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Start reading Differential Geometry of Curves and Surfaces on your Kindle in under a minute .

## Who are some famous students of do Carmo?

Do Carmo is also known for his textbooks. They were translated into many languages and used in courses from universities such as Harvard and Columbia. His students included Celso Costa, Marcos Dajczer and Keti Tenenblat.