Periodic Conjugate Nets
Periodic Conjugate Nets
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Necessary conditions on the coefficients of the point equation of A^ are derived and it is shown by discussion of the completely integrable systems of partial differential equations involved that these conditions are also sufficient. It is also shown that if an equation of Laplace of form (1) is the point equation of one periodic net, it is the point equation of an infinity of others of the same period. The remainder of the paper is taken up with other sequences of Laplace * Here xi indicates a...ny or all of a;i, . . . , a;/"\ A similar usage is followed throughout, t Darboux, Logons sur la thcoric generale des surfaces, 2d ed. (1915), vol. II, chap. 2. 238 4 4 4 o n r> 239 EDWARD S. HAMMOND. closely related to the sequence Nr. The sequences studied in section 3 involve certain properties of families of lines in higher ordered spaces which we pi:ocee'4^'Y = U{u')VW)['^p'V, where U and V are the transforms of U and T' under (7). Hence and \p may be determined so that H'Hi • • • H p-i =1; then from (32), X equals a constant, * w, since d log X _ ^ogj^ _ du dv In the remainder of this section, we shall assume that this transformation has been made, dropping primes for convenience.
What to read after Periodic Conjugate Nets?
You can find similar books in the "Read Also" column, or choose other free books by Edward Sanford Hammond to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Necessary conditions on the coefficients of the point equation of A^ are derived and it is shown by discussion of the completely integrable systems of partial differential equations involved that these conditions are also sufficient. It is also shown that if an equation of Laplace of form (1) is the point equation of one periodic net, it is the point equation of an infinity of others of the same period. The remainder of the paper is taken up with other sequences of Laplace * Here xi indicates a...ny or all of a;i, . . . , a;/"\ A similar usage is followed throughout, t Darboux, Logons sur la thcoric generale des surfaces, 2d ed. (1915), vol. II, chap. 2. 238 4 4 4 o n r> 239 EDWARD S. HAMMOND. closely related to the sequence Nr. The sequences studied in section 3 involve certain properties of families of lines in higher ordered spaces which we pi:ocee'4^'Y = U{u')VW)['^p'V, where U and V are the transforms of U and T' under (7). Hence and \p may be determined so that H'Hi • • • H p-i =1; then from (32), X equals a constant, * w, since d log X _ ^ogj^ _ du dv In the remainder of this section, we shall assume that this transformation has been made, dropping primes for convenience.
What to read after Periodic Conjugate Nets?
You can find similar books in the "Read Also" column, or choose other free books by Edward Sanford Hammond to read onlineMoreLess
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