# Second fundamental form

## Definition

Let be a manifold embedded in . the **second fundamental form** on is the map defined as follows:

where si the Levi-Civita connection of and is the Levi-Civita connection on .

Let be a manifold embedded in . the **second fundamental form** on is the map defined as follows:

where si the Levi-Civita connection of and is the Levi-Civita connection on .