By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in ${Bbb R}^{n+d},$ $n ge 2$, $d ge 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian $n$-manifolds into ${Bbb R}^{n+d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the cases of surfaces in ${Bbb R}^3$.
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机译：通过使用E. Cartan的等价方法，我们计算了黎曼2-流形的局部标量不变量。我们还根据局部等距嵌入方程的对称性，定义了$ { Bbb R} ^ {n + d}，$ $ n ge 2 $，$ d ge 1 $中子流形的局部不变量的概念黎曼$ n $流形变成$ { Bbb R} ^ {n + d} $。我们表明，在$ { Bbb R} ^ 3 $曲面的情况下，通过Cartan方法获得的局部不变量是我们所知的局部不变量的内在表达式。
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