# Geometric Calculus of the Gauss Map

## TL;DR

This paper bridges classical differential geometry with geometric calculus, introducing a generalized Laplacian for multivector functions on manifolds and extending Jacobi's equation to higher codimensions.

## Contribution

It presents a novel integration of geometric calculus into differential geometry and develops a higher codimensional Jacobi field equation.

## Key findings

- Defined a generalized Laplacian for multivector functions
- Formulated a higher codimensional Jacobi's field equation
- Connected classical geometry with geometric calculus

## Abstract

In this paper we connect classical differential geometry with the concepts from geometric calculus. Moreover, we introduce and analyze a more general Laplacian for multivector-valued functions on manifolds. This allows us to formulate a higher codimensional analog of Jacobi`s field equation.