For further reading we recommend the very interesting textbook: M. P. do Carmo, Riemannian Geometry, Birkhauser (1992). I am very grateful to my many students who throughout the …

Preface These are notes for the lecture course \Di erential Geometry I" held by the second author at ETH Zurich in the fall semester 2010. They are based on a lecture course held by the rst …

Context-Aware Evaluation via CARMO Our proposed framework, CARMO, addresses these lim- itations by autonomously generating dynamic, task- specific criteria for both absolute and …

The tangent line intersects the plane y = 0 when r = −t/2, but 3t + 3r 6= 2t3 + 6rt2 for this value of r. Evidently, when do Carmo talks about the angle between two lines he means the angle …

On page 2 do Carmo says that the interval I should be open but on page 30 he extends the notion of smoothness to closed intervals. A function defined on a closed interval [a, b] is said to be …

Here do Carmo uses the notation hw1; w2i for what was denoted by w1 w2 in Chapter I and calls hw1; w2i the inner product (rather than the dot product) of the vectors w1; w2 2 R3.

t mean curvature immersed in a space of nonnegative constant curvature. On the other hand, Chern-do Carmo-Kobayashi [1] have obtained a classi-fication theorem for submanifolds with …