I'm looking at this paper 'Boundary conditions at a liquid-vapor interface' by Prosperetti 1979 and on the second page this definition is given for the total curvature:
The total curvature $\mathscr{C}$ of the interface at a point $P$ is defined by
$\mathscr{C} = \frac{1}{R} + \frac{1}{R'}$
where $R$ and $R'$ are the radii of curvature of the sections of the interface with any two planes orthogonal to each other and to the interface at $P$.
I'm not too familiar with differential geometry but this seems pretty different from the usual definition of total curvature and it's also not the same as Gaussian curvature which would be the product instead of the sum. Is there another better-known name for this curvature term?
Edit: interface here refers to a surface. The context being the 'interface' between a liquid and a vapor.