Annalisa Calvi

Corollaries of the Gauss-Bonnet Theorem for Surfaces in R^n

The Gauss-Bonnet theorem implies that the total curvature of a surface depends only on the topology of a surface; in particular, on its Euler characteristic. Then, curvature can be expressed in terms of the second fundamental form, which is then inside a surface integral equal to a topological constant. We intend to vary this surface integral and investigate the resulting equation, as we conjecture that we will be able to derive fundamental equations of submanifold geometry.

Annalisa Calvi

Monash University

Annalisa Calvi is studying the Bachelor of Science Research – Advanced course at Monash
University, majoring in pure mathematics and computer science. She is keen on a career in mathematics research, and is figuring out which area of mathematics is her favourite. This is difficult because from what she has seen so far, they are all similarly interesting and beautiful. Outside of her studies, Annalisa teaches undergraduate computer science.

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