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We construct frustrated antiferromagnetic spin ladders with m chains forwhich the exact ground state can be determined in a particular parameterregime. The excitation spectrum is shown rigorously to be gapless ( with gap )for odd ( even ) m. In a general parameter regime, the four-chain and periodicladders are studied using a mean-field theory based on the bond operatorformalism for spin $S=1/2$. The excitation spectrum and the spin-gap arecalculated in both the cases. The spin-gap of the frustrated ladder system hasa larger magnitude than in the case of non-frustrated ladders. For thefrustrated periodic ladder, the spin-gap vanishes at a critical value of theinterladder coupling strength which is larger than the critical value in thecase of non-frustrated periodic ladder.Comment: 22 pages, LaTeX, 6 figures available upon request, submitted to Phys.  Rev.

Antiferromagnetic spin ladders with odd and even numbers of chains